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A Quality Function Deployment (QFD) Approach for Bridge Maintenance Management Bolar, Aman Ahmed 2014

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A QUALITY FUNCTION DEPLOYMENT (QFD) APPROACH FOR  BRIDGE MAINTENANCE MANAGEMENT  by Aman Ahmed Bolar  B.E., Bangalore University, 1996 M.Eng., Memorial University of Newfoundland, 2001  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE COLLEGE OF GRADUATE STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)  July 2014  © Aman Ahmed Bolar, 2014 ii Abstract Infrastructure age in the US/Canada are beyond half their expected service life. With billions of dollars invested annually, an increase in number of decisions towards maintenance, rehabilitation and replacement (MRR) activities are expected. Customer (infrastructure user) opinions are sometimes sought when major infrastructure-related decisions are made by conducting surveys, community meetings, etc. However, with consumers becoming more involved in economic, environmental, and social issues related to infrastructure, a process for ensuring customer demands are addressed would be valuable to all stakeholders involved. In this thesis, using bridge as an example, an innovative expert-based decision-framework has been proposed and developed using the Quality Function Deployment (QFD) approach. The framework comprises of three major elements. First a hierarchical evidential reasoning (HER) framework is proposed and developed for condition assessment of bridges by classifying bridge elements into Primary, Secondary, Tertiary and Life Safety-Critical elements. Respective indices are calculated in addition to an overall bridge condition index. The HER framework enables combining different distress indicators and propagating both aleatory/epistemic uncertainties using either Dempster-Shafer or Yager's rule. Importance and reliability factors (collectively termed "credibility factor") are introduced based on bridge element importance and reliability of collected data. Second, QFD implementation has been demonstrated with the following applications: (i) Inspection Prioritization (ii) Decision-Making between Replacement and/ or Rehabilitation scenarios. For inspection prioritization, an Inspection House of Quality is prepared for translating consumer demands (WHATs) into inspection requirements (HOWs) and demonstrated using data developed from Colorado Department of Transportation (CDOT) inspection manual. For the decision-iii making scenarios, a case study is furnished for a bridge located in Victoria, BC. Finally. the infrastructure-user's expectations are dynamic given the changing economic conditions, technologies, environmental regulations, etc. A hidden Markov model (HMM) is utilized for predicting such dynamic customer response by using probabilities of focus areas that are of interest to the infrastructure-user as hidden parameters. Using the 2005 California Transportation's customer survey, a case study is presented for demonstrating the application.  This new expert-based framework has an ability to enhance decision-making by addressing uncertainty in collected inspection data, facilitating customer input into MRR procedures and by predicting customer expectations. iv Preface The research presented in this thesis was done by me under the supervision of Drs. Solomon Tesfamariam and Rehan Sadiq. The research work was also published (or submitted) in international peer-reviewed journals with my supervisors as co-authors. I prepared the manuscripts and was corresponding author for all the publications. The manuscripts were reviewed by my supervisors and I incorporated relevant feedback before submitting to the journal for review. Reviewing correspondence from the journal, article proofs, and responding to comments was done by me in consultation with my supervisors.  List of publications are: A version of Chapter 3 has been published: Bolar, A., Tesfamariam, S., & Sadiq, R. (2012). Condition assessment for bridges: A hierarchical evidential reasoning (HER) framework. Structure and Infrastructure Engineering, 9(7): 648-666.   A version of Chapter 4 has been published: Bolar, A., Tesfamariam, S., and Sadiq, R. (2013).  Management of Civil Infrastructure Systems: A QFD-Based Approach. ASCE Journal of Infrastructure Systems 20 (1).  A version of Chapter 5 has been submitted and is under review: Bolar, A., Tesfamariam, S., and Sadiq, R. (2014).  Predicting infrastructure user response for quality function deployment (QFD) using hidden Markov model. ASCE Journal of Infrastructure Systems (Under review).  The QFD implementation using independent scoring method in Chapter 2 also appears in: v Bolar, A., Tesfamariam, S., and Sadiq, R. (2012b). "Quality Function Deployment (QFD) for Bridge Maintenance." CSCE 1st International Specialty Conference on Sustaining Public Infrastructure: Decision Making-Prioritization and Optimization, Edmonton, AB, June 6-9, 2012  vi Table of Contents  Abstract ..........................................................................................................................................ii Preface ........................................................................................................................................... iv Table of Contents .......................................................................................................................... vi List of Tables ................................................................................................................................. xi List of Figures ............................................................................................................................ xiii List of Illustrations ...................................................................................................................... xv List of Symbols ............................................................................................................................ xvi List of Abbreviations ............................................................................................................... xviii Acknowledgements ..................................................................................................................... xxi Chapter  1: Introduction ............................................................................................................... 1 1.1 Background ............................................................................................................ 1 1.2 Bridge Maintenance ............................................................................................... 4 1.3 Decision-Making for Bridge Management ............................................................ 6 1.4 Research Motivation .............................................................................................. 7 1.5 Research Objectives............................................................................................... 8 1.6 Thesis Organization ............................................................................................... 9 Chapter  2: Literature Review.................................................................................................... 12 2.1 Maintenance History ............................................................................................ 12 2.2 Bridge Management Systems (BMS) .................................................................. 13 2.2.1 General ................................................................................................................. 13 2.2.2 Condition Assessment of Bridges ........................................................................ 14 vii 2.2.3 Pontis® - The United States BMS ........................................................................ 15 2.2.4 BMS in Canada .................................................................................................... 18 2.2.5 BMS in Australia and New Zealand .................................................................... 20 2.2.6 Japanese Bridge Management System (JBMS) ................................................... 20 2.2.7 South African Bridge Management System ........................................................ 21 2.2.8 European Bridge Management System ............................................................... 21 2.3 Uncertainty Handling in Bridge Maintenance ..................................................... 23 2.3.1 Uncertainty Sources & Analysis Techniques ...................................................... 23 2.3.2 Soft Computing Methods for Bridge Condition Assessment .............................. 26 2.3.3 Dempster-Shafer Theory of Evidence ................................................................. 28 2.3.4 Dempster-Shafer (DS) rule of combination ......................................................... 29 2.3.5 Yager Modified Dempster-Shafer (DS) rule of combination .............................. 31 2.4 Decision-Making in Bridge Maintenance ............................................................ 32 2.5 Quality Function Deployment ............................................................................. 33 2.5.1 The QFD Process ................................................................................................. 35 2.5.2 Prioritization Techniques for QFD ...................................................................... 38 2.5.3 Rating Systems for QFD ...................................................................................... 39 2.6 Predicting Customer Requirements ..................................................................... 41 2.6.1 Hidden Markov Model in Civil Engineering Problems ....................................... 42 2.6.2 Dealing with Dynamic Customer Requirements in QFD .................................... 42 2.7 Proposed Approach .............................................................................................. 43 Chapter  3: Hierarchical Evidential Reasoning (HER) Framework for Condition Assessment of Bridges ................................................................................................................. 45 viii 3.1 Background .......................................................................................................... 45 3.2 Bridge Hierarchical Evidential Reasoning (HER) Framework ........................... 49 3.2.1 Bridge Management Systems (BMS) .................................................................. 49 3.2.2 HER Based Health Indices .................................................................................. 50 3.3 Basic HER framework ......................................................................................... 53 3.4 Application of HER Framework .......................................................................... 61 3.4.1 Illustrative Evaluation of Secondary Condition Index: D-S Rule of Combination ........................................................................................................ 66 3.4.2 Illustrative Evaluation of Secondary Condition Index: Yager Rule of Combination ........................................................................................................ 68 3.4.3 Evaluating an Overall Bridge Condition Index (BCI) ......................................... 69 Chapter  4: Quality Function Deployment for Infrastructure Management ......................... 72 4.1 Background .......................................................................................................... 72 4.2 Application of QFD in Infrastructure Management ............................................ 75 4.2.1 Framework for Infrastructure Inspection Prioritization using QFD .................... 75 4.2.2 Framework for Infrastructure Management Decision-Making Using QFD ........ 78 4.3 Bridge Inspection Prioritization using Quality Function Deployment ................ 78 4.3.1 HOWs and WHATs ............................................................................................. 79 4.3.2 Relationship Matrix ............................................................................................. 84 4.3.3 Correlation Matrix ............................................................................................... 84 4.3.4 Discussion ............................................................................................................ 86 4.4 Bridge Maintenance Management using QFD .................................................... 86 ix Chapter  5: Infrastructure User Requirements in QFD using a Hidden Markov Model (HMM) .......................................................................................................................................... 97 5.1 Background .......................................................................................................... 97 5.1.1 Preliminaries: Markov Chain Basics ................................................................... 97 5.1.2 Implementing Hidden Markov Model for QFD ................................................ 100 5.2 Application of QFD HMM to Infrastructure Maintenance................................ 103 5.2.1 Customer Response Analysis: Case study ......................................................... 103 5.2.2 Observed Probabilities for Focus Areas ............................................................ 104 5.2.3 Discussion .......................................................................................................... 111 Chapter  6: Conclusions and Recommendations .................................................................... 114 6.1 Summary ............................................................................................................ 114 6.2 Specific Contributions - Chapter 3 .................................................................... 115 6.3 Specfic Contributions - Chapter 4 ..................................................................... 116 6.4 Specific Contributions - Chapter 5 .................................................................... 117 6.5 Limitations of this Research .............................................................................. 117 6.6 Recommendations.............................................................................................. 118 Bibliography ............................................................................................................................... 119 Appendices ................................................................................................................................. 134 Appendix A: Condition Assessment using Hierarchical Evidential Reasoning (HER)  Framework ......................................................................................................... 134 A.1 Frame of Discernment & Ignorance Computation Examples............................ 134 A.2 Combining Two Bodies of Evidence using Dempster Rule .............................. 135 Appendix B: Management of Civil Infrastructure Systems - a QFD-Based Approach .......... 138 x B.1 Frame of Discernment & Ignorance Computation Examples............................ 138 Appendix C: Microsoft Excel Visual Basic Application (VBA) Code for Hidden Markov Implementation .................................................................................................. 147 xi List of Tables  Table 2-1 Colorado Department of Transportation (CDOT) Pontis® Elements .................... 17 Table 2-2 Summary of Canadian Provincial BMS Features .................................................. 19 Table 2-3 Summary of European BMS Features .................................................................... 23 Table 2-4 Soft Computing Methods in Bridge Condition Assessment .................................. 27 Table 2-5 Fundamental scale used to developing matrix for AHP (Saaty, 1988) .................. 40 Table 3-1 Application of Soft Computing to Bridges ............................................................ 48 Table 3-2 Condition evaluation granularity in BMS/research [Reported by Wang (2008)] .. 53 Table 3-3 The D-S Rule of Combination for Two Bodies of Evidence ................................. 54 Table 3-4 Proposed classification of the Colorado Department of Transportation (CDOT) Pontis® Elements ................................................................................................. 58 Table 3-5 Proposed classification of the Colorado Department of Transportation (CDOT) Pontis® SmartFlags .............................................................................................. 59 Table 3-6 Mapping of data from Liang (2001) to proposed HER framework ....................... 64 Table 3-7  Credibility factors and criteria for classifying bridge elements used in Liang (2001) .................................................................................................................... 65 Table 4-1 Relating Hypothetical Survey to Pontis® Elements .............................................. 80 Table 4-2  Colorado Department of Transportation (CDOT) Pontis® Elements ................... 82 Table 4-3 Priority Ranking of Pontis® Inspection Items Using House of Quality Absolute Weights ................................................................................................................. 83 Table 4-4 WHATs vs. HOWs Correlation Scale .................................................................... 84 Table 4-5 Johnson Bridge QFD Decision-Making Scenarios ― Description of HOWs ....... 89 xii Table 4-6 Results from HOQ for Johnson Bridge - Independent Scoring Method ................ 95 Table 4-7 Results from HOQ for Johnson Bridge - Lyman's Normalization ......................... 95 Table 4-8 Results from HOQ for Johnson Bridge - Wasserman's Normalization .................. 95 Table 5-1 Mapping of CALTRANS Linguistic Data to Numerical Rating System ............. 108 Table 5-2 Customer Requirement States .............................................................................. 109 Table 5-3 Expert Opinion on Transition/Emission Probabilities ......................................... 110 Table 5-4 Summary of Customer Requirements from 2-Step Hidden Markov Analysis..... 112 Table B-1 Prioritizing product characteristics using Independent Scoring Method: an exaggerated example .......................................................................................... 143 Table B-2 Prioritizing product characteristics using Lyman's Normalization Method: an exaggerated example .......................................................................................... 144 Table B-3 Prioritizing product characteristics using Wasserman's Normalization Method: an exaggerated example .......................................................................................... 145 Table B-4 Matrix of correlations between product characteristics (HOWs) in the scale [0,1]: an exaggerated example ...................................................................................... 146  xiii List of Figures  Figure 1-1 Average Age of Canadian Public Infrastructure ..................................................... 5 Figure 1-2 Thesis Organization .............................................................................................. 11 Figure 2-1 Components of a BMS .......................................................................................... 16 Figure 2-2 QFD Process Flowchart ........................................................................................ 36 Figure 2-3 House of Quality (HOQ) ....................................................................................... 37 Figure 2-4 Proposed Approach ............................................................................................... 44 Figure 3-1 Generic Bridge Hierarchical Evidential Reasoning (HER) Framework ............... 56 Figure 3-2 Huey-Tong Bridge Data from Liang (2001) in Proposed Hierarchical Evidential Reasoning (HER) Framework .............................................................................. 63 Figure 4-1 Infrastructure Inspection Prioritization and Maintenance Decision-Making using QFD ...................................................................................................................... 76 Figure 4-2 Inspection HOQ for Inspection Prioritization - Wasserman's Normalization ...... 85 Figure 4-3 Typical HOQ for Johnson Bridge using Independent Scoring: Rehabilitation Option - Residents Response (RehR) ................................................................... 90 Figure 4-4 Typical HOQ for Johnson Bridge using Lyman's Normalization: Rehabilitation Option - Business Response (RehB)..................................................................... 91 Figure 4-5 Typical HOQ for Johnson Bridge using Wasserman's Normalization: Replacement Option - Resident's Response (Rep) ............................................... 92 Figure 4-6 Independent Scoring Results:  HOQ for Johnson Bridge using: Rehabilitation Option - Residents Response (RehR) ................................................................... 94 xiv Figure 4-7 Lyman's Normalization Results: HOQ for Johnson Bridge using Rehabilitation Option - Business Response (RehB)..................................................................... 94 Figure 4-8 Wasserman's Normalization Results:  HOQ for Johnson Bridge using: Replacement Option - Resident's Response (RepR) ............................................. 94 Figure 5-1 Markov Chain Transition Possibilities from time (t-1) to (t) ................................ 99 Figure 5-2 Customer Requirement (Relative Importance) Obtained using Hidden Markov Analysis .............................................................................................................. 113 Figure A-1 An Example of Combining Two Bodies of Evidence Obtained from Bridge Inspection ............................................................................................................ 137    xv List of Illustrations Illustration 1-1 The scene at the I-35W Mississippi River Bridge, the first morning after its collapse by Mike Wills, retrieved from http://en.wikipedia.org/wiki/File:I35_Bridge_Collapse_4crop.jpg Used under Creative Commons Attribution-ShareAlike 2.0 Generic license (http://creativecommons.org/licenses/by-sa/2.0/deed.en)   .............................. 4xvi List of Symbols A  subset of Θ B  subset of Θ Cre  credibility factor in hidden Markov model ike   i parameters related to k attributes )2(kIe   Results of 21 kk ee ⊕  Ek  evaluated combined attribute Es  evaluation for attribute s  F  transition probability matrix with initial probability H  condition state Hn   subset to power set H i  parameters in HER framework; number of attributes related to WHAT in    QFD;  condition state in hidden Markov model j  parameter related to condition state; number of attributes related to HOW in   QFD;  number of condition states in hidden Markov model k  number of attributes K  conflict between sets A & B LK  number of parameters that contribute to the kth attribute m  mass probability assignment; subscripts represent subset number M  number of bodies of evidence n  number of steps in Markov process N  number of condition states oj  j observed parameters xvii O  set of observed parameters 𝑃  probability QO  quality offered rij  cardinal relationship constituting the relationship matrix s  condition states (subscript represents number) sj  j condition states S  set of condition ratings t  time V  observed probabilities matrix 𝑋𝑡  stochastic process at time t {X}  Markov chain Θ  Frame of Discernment Ψ  subset of Θ and intersection of sets A and B Φ  null (empty) set ⊕  operator for Demstper-Shafer (D-S) rule of combination ε  element of ⊆   (subset with) fewer or equal elements ∀  for all λ   credibility factor βn,i  degree of confidence (n numbers with i attributes) xviii List of Abbreviations AASHTO American Association of State Highway and Transportation Officials AHP   Analytical Hierarchy Process ASCE  American Society of Civil Engineers ASR   Alkali-Silica Reactivity BAMS  Bridge Asset Management System BCI   (overall) Bridge Condition Index  BMS  Bridge Management System BPA  Basic Probability Assignment BREX  Bridge Expert Rating System BRIME Bridge Management in Europe BTS   Bureau of Transportation Statistics CC  Condition Class CDOT  Colorado Department of Transportation CoRe  Commonly Recognized COST   Co-operation in the Field of Scientific and Technical Research CPI  Core Public Infrastructure CR  Customer Requirements CRM  Customer Relationship Management CS  Condition State DS  Dempster-Shafer DST   Dempster-Shafer theory ER  Evidential Reasoning xix ERA   Environmental Risk Assessment FECM  Federation of Canadian Municipalities FHWA  Federal Highway Administration FP  (European) Framework Program FP4  Fourth (European Bridge) Framework Program FP5  Fifth Framework Programs FP7  Seventh (European) Framework Program FWA  Fuzzy Weighted Average GDP   gross domestic product HER   Hierarchical Evidential Reasoning  HMM  Hidden Markov Model HOQ   House of Quality  HS  Highway Semi  IHOQ  Inspection House of Quality ISTEA  Intermodal Surface Transportation Efficiency Act JBMS  Japanese Bridge Management System KM  Knowledge Management LCC  Life Cycle Costing LMS  Life-Cycle Management System MADM Multi-Attribute Decision Making MCDM Multi-Criteria Decision Making MGI  McKinsey Global Institute MODM Multi Objective Decision Making MMM  Modified Mountain Clustering Method  xx MRR   Maintenance, Repair and Rehabilitation NBI   National Bridge Inventory  NBIS  National Bridge Inspection Standards NCHRP  National Co-operative Highway Research Program  NDOT  Nevada Department of Transportation NLP   Non Linear Programming  PEI  Prince Edward Island QA/QC  Quality Assurance/Control  QFD  Quality Function Deployment RehB  Rehabilitation Option - Business's Response REH-HOQ Rehabilitation House of Quality RehR  Rehabilitation Option - Resident's Response RepB  Replacement Option - Business's Response REP-HOQ  Replacement House of Quality RepR  Replacement Option - Resident's Response RWA  Roadway Alignment SANRAL South African Roads Agency Limited SCI   Secondary Condition Index  SR  Sufficiency Rating TPM   Transition Probability Matrix US  United States VBA   (Microsoft-Excel) Visual Basic Application   xxi Acknowledgements First and foremost, many thanks to the Almighty God for everything; from giving me the courage to undertake this program, persistence during the research, and perseverance towards completion. I would like to extend my gratitude to my supervisor Dr. Solomon Tesfamariam and co-supervisor Dr. Rehan Sadiq for providing me with an opportunity to explore and grow in the exciting field of risk assessment and decision sciences. From start to finish, you have been a great source of technical feedback.  Their encouragement and guidance, without doubt, has helped me in completing my research and this thesis.  I am also thankful to the committee members Dr Kasun Hewage, Dr. Shahria Alam and Dr. Rudolf Seethaler who offered their observations and assessment especially during the proposal defense.  I also sincerely thank UBC Okanagan for financial support by the way of tuition waiver. Many thanks are due to administrative staff who patiently clarified and addressed any queries.  Lastly, my deepest appreciation to my wife for her patience and always being by my side through this journey.  Also, my daughter, who had to sacrifice her bonding years for me to accomplish this goal. Thank you both.      1 Chapter  1: Introduction 1.1 Background The term "infrastructure" is defined in the oxford dictionary1The total value of North American infrastructure systems is estimated to be $33 trillion. The yearly average investment on infrastructure is estimated to be $53 and $303 billion in Canada and the United States (US), respectively (Elbehairy 2007). A study done by the McKinsey Global Institute (MGI 2013) has estimated that about $57 Trillion is required by the year 2030 just to keep up with gross domestic product (GDP) growth, which is a standard measure of economy. In North America, infrastructure report cards are currently utilized to provide a grade, analogous to schooling system, wherein the evaluated condition and performance of infrastructure is reported.   as: "the basic physical and organizational structures and facilities (e.g. buildings, bridges, roads, and power supplies) needed for the operation of a society or enterprise." Within the civil engineering and construction industry, infrastructure is a term more commonly adapted to structures and related entities owned by the government (municipal, provincial or federal) for serving citizens and can sometimes be termed as public infrastructure, which include roads, rails, bridges, arenas, parks, etc. (Miller 2000).  For the United States, the American Society of Civil Engineers (ASCE) introduced the infrastructure report card in the year 1988. The report card contains an evaluation using five ratings “A” through “D” and “F” (where A=Exceptional; F= Failing), for each infrastructure category in the country. The 1988 report had defined eight infrastructure categories and since                                                  1 http://oxforddictionaries.com/definition/infrastructure    2 then five report cards have been published, the most recent in the year 2013 (ASCE 2013). In addition, in the year 2011, “Failure to Act” documents were published by the ASCE with the objective of reporting the economic implications of current US investment trends in key infrastructure sectors. The 2013 report card has sixteen infrastructure categories and the overall rating for America's infrastructure is "D+" (Poor, but leading to Mediocre). The cost to improve infrastructure is estimated as $3.6 Trillion in a 7-year period which translates into a budget of about $514 billion per year. Compared to the $3562Comparing the last three report cards (2005, 2009 & 2013), the overall infrastructure rating has improved from D to D+.  A few other transportation related infrastructure have been performing as follows:  billion budget, a $158 billion annual deficit exists in the US infrastructure budget.   Aviation: Fall in grade from D+ to D   Bridges: Improved from C to C+.    Rail:  Improved from C- to C+   Roads:  Remains at D, but fell to D- in 2009 In Canada, the first report card was published in the year 2012 for municipal infrastructure that includes water/wastewater systems and municipal roads excluding bridges and culverts, etc. (Félio 2012; www.canadainfrastructure.ca). The rating systems used were (meaning of the rating in brackets): very good (fit for the future), good (adequate for now), fair (requires attention), poor (at risk), and very poor (unfit for sustained service).  The condition of municipal roads was rated as fair (meaning requires attention), while water/wastewater, and storm water received                                                  2 http://www.cbo.gov/publication/25116   3 good and very good ratings, respectively. The replacement cost of the deficient infrastructure alone is $171 Billion. Prior to 2012, reports published by the Federation of Canadian Municipalities (FECM) provided information about the condition of infrastructure. A report published in 2007 titled "Danger Ahead: The coming collapse of Canadian Infrastructure" highlighted that deferred investments in maintenance has caused the deficit to reach $123 Billion compared to about $12 Billion in the year 1985 (Mirza 2007). Also recently, a model framework for Canada's Core Public Infrastructure’s (CPI) performance measures was published by Félio and Lounis (2009). CPIs include roads, transit, bridges, and water & wastewater infrastructure. Currently, Statistics Canada reports condition of infrastructure in the context of percentage of useful life expended by the infrastructure. The average age of Canadian CPI as a percentage of useful life is shown in Figure 1-1. The average age of Canadian Infrastructure peaked to 17.2 years in the year 2000. A steady increase in federal funding during 2000-2009 resulted in an average age of 15.2 years in the year 2009. The current stimulus funding as a result of the economic crisis has provided $33 billion in funding that is expected to peak in the year 2011-2012 and decrease gradually when the funding ends in 2014 (Infrastructure Canada 2011). Since infrastructure types include various structural entities, to set a focal point for the current study, bridge structures were selected. The current state of bridges in the US as rated in ASCE (2013) is "C+" which refers to mediocre (requires attention), but leading to "good for now" state. The report also provides the average bridge age as 42 years compared to their service life of 50 years. Referring to Figure 1-1, the average age of Canadian bridges is 24.5 years compared to their mean service life of 43.3 years (Statistics Canada 2007).    4 1.2 Bridge Maintenance Bridges provide a means of transition over obstacles, such as valley, waterway or between hills, and failure could lead to a disintegrated network (Illustration 1-1) apart from compromises in public safety and economic losses. Compared to the other CPI categories, bridges are perhaps one of the most complicated assets, given their inspection and maintenance requirements.   Illustration 1-1 The scene at the I-35W Mississippi River Bridge, the first morning after its collapse by Mike Wills, retrieved from http://en.wikipedia.org/wiki/File:I35_Bridge_Collapse_4crop.jpg Used under Creative Commons Attribution-ShareAlike 2.0 Generic license (http://creativecommons.org/licenses/by-sa/2.0/deed.en) The preferred method of inspection for bridges is visual inspection thereby relying on bridge inspectors for condition reporting. The inspection is normally done every two years and interim   5 inspections may be carried our depending on problem areas (White et al. 1992). Sensors are used for "health monitoring" of bridges only for special cases due to cost limitations (Wu and Yokoyama 2006). A bridge inspector therefore has to be familiar with the various aspects of bridges such as types (steel, concrete, timber) in addition to deterioration types such as fracture        Figure 1-1 Average Age of Canadian Public Infrastructure3critical elements in the case of steel bridges (Hao 2010). Furthermore, the inspector could be faced with multidisciplinary issues. For example, hydraulics knowledge would be essential when dealing with bridges under water in order to determine scouring effects (White et al. 1992). Similarly, specialized inspection personnel may be required for a bascule type bridge having mechanical components. Such requirements are absent in other infrastructure categories such as roads, water treatment facilities, etc. With regards to maintenance, bridge damages bear higher level of uncertainty given that they sustain varying traffic loads in addition to loads from naturally occurring events. Once the damage and condition states are established, rectification process may involve repairs during bridge operation or by suspending traffic. Again, these challenges are solely attributed to bridges compared to other infrastructure types. This is the                                                   3 http://www.statcan.gc.ca/pub/11-621-m/2008067/tables/5002061-eng.htm   6 reason bridges have always been a starting point for the development of infrastructure management systems (Adey et al. 2010). Similar to other infrastructure categories, bridges undergo aging and deterioration with time caused by a variety of mechanisms. For example, corrosion of reinforcing steel is today’s leading cause of deterioration of reinforced concrete structures in North America. Moreover, the causes of deterioration can be operational (loading, number of passes, wear/tear), natural events, environmental effects (exposure to corrosive environment or freeze/thaw cycles), quality of construction, age, geometry and material of the bridge, etc. Each of these parameters can individually or collectively lead to deterioration and contribute in a different way to overall failure. Therefore, bridge maintenance involves collecting a large body of data from various sources and requires expert judgment in making a maintenance decision (Bolar et al. 2012a).  1.3 Decision-Making for Bridge Management Bridge maintenance is an elaborate process that aims at addressing various demands (e.g., anticipated increase in external loads, enhanced aesthetics) that are subject to different constraints (e.g., design capacity could be a constraint for increase in external loads; limited funding could be an economic constraint for enhancing aesthetics). In other words, engineering demands are those that are deemed essential for the safe use of the infrastructure, the design of which is assured by complying with design codes and regulations set by engineering standards. Once built and under operation, in-service usage and exposure to deleterious reactions can deteriorate the infrastructure with time. Therefore, inspection programs are normally established to help identify the deterioration process early on and thereby proactively control risk that would arise due to unattended maintenance.  While engineering demands can intuitively cause concerns to any user, consumer demands normally involve sustainability issues and could be more   7 elaborate. For example, for a bridge user, safety and engineering would definitely be a concern, but the demands are much different in form such as expectations of the bridge under operation. The expectations need not just be intrinsic such as riding comfort, but lately with consumers becoming more involved in economic, environmental, social, etc., issues related to infrastructure the list of demands is not limited. The consumer need not be limited to the bridge user alone, but anyone that can get affected by the bridge operation such as corporate entities, general public, authorities such as fire rescue, airports, ports, etc., can all have interest in the bridge operation and usage. Infrastructure maintenance-related activities supplement asset management systems wherein infrastructure preservation, upgrading, and replacement decisions are facilitated in the context of cost optimization and  resource allocation (FHWA 1999). In this thesis the scope of the study is limited to maintenance, rehabilitation and replacement (MRR) activities alone and hence the terms "management", "maintenance", and "maintenance management" would imply an MRR activity. 1.4 Research Motivation As explained in Section 1.2, bridge maintenance involves collecting a large body of data for decision-making leading to further action that is required in order to minimize risk. In the case of visual inspection, for example, the process of data collection involves subjective judgment of the inspector in reporting condition and is therefore accompanied by a high level of uncertainty. Furthermore, the process of aggregating the collected information for condition assessment requires use of uncertainty handling techniques. Review of existing bridge management systems (BMSs) confirmed that current bridge maintenance practices lack some of the aforementioned features and improvements can be made by including uncertainty propagation in the condition assessment model. Referring to Section 1.3, customer involvement can add value to maintenance   8 decision-making.  While customer involvement is possible by means of community engagement meetings, surveys, informational meetings, focus groups, etc., the obtained customer feedback would require a process for ensuring the maintenance decisions carried out adequately address customer concerns. In other words, having a process where customer requirements can be translated into maintenance specifications would immensely aid the decision-making process. The end user of the infrastructure is the customer and ensuring customer feedback has complemented the maintenance decision-making would be valuable to all stakeholders involved especially when important infrastructure-related decisions such as a replacing major bridge, new road developments, etc are being considered by infrastructure agencies.  One such process that is widely used in the manufacturing industry for translating customer requirements into design specifications is called as quality function deployment (QFD). Review of infrastructure decision-making procedures indicated limited use of QFD in infrastructure or civil engineering. This further motivated the use of QFD for the current study. In addition, since the use of QFD requires customer input, techniques for predicting customer response by using existing customer surveys is also proposed in this thesis. 1.5 Research Objectives The objective of this thesis is to develop an improved approach for infrastructure management systems thereby providing the decision-maker an effective tool to evaluate, control and mitigate risk effectively. In particular, the improved approach will consist of an integrated decision making framework with the following specific objectives: 1. Incorporate improved epistemic uncertainty handling techniques for condition assessment that can address subjective, imprecise, incomplete and conflicting data.   9 2. Incorporate customer (infrastructure-user) requirements in the decision making process involving maintenance, rehabilitation and replacement (MRR) of infrastructure. 3. Incorporate a tool that can aid in forecasting of infrastructure-user requirements 1.6 Thesis Organization The thesis has been organized into six chapters as shown in Figure 1-2 and described as follows: Chapter 1:  Contains an introduction to infrastructure maintenance with a focus on bridges; Research motivation and thesis organization have been presented. Chapter 2:  Contains literature review of the following topics:  North American & International BMS  Uncertainty related to BMS  Decision-making in Bridge Maintenance  Quality Function Deployment At the end of this chapter, framework of the proposed approachChapter 3:  Contains a study that can address uncertainty issues in bridge condition assessment by using a hierarchical evidential reasoning (HER) framework thereby achieving objective 1 (Section 1.5). Using a case study, a practical application is presented by mapping existing data to the current HER framework thereby demonstrating that existing bridge practices can easily be accommodated in the proposed framework.   is presented. Chapter 4: Contains a study that can address lacking of customer involvement in bridge maintenance decision making thereby achieving objective 2 (Section 1.5). Using Quality Function Deployment (QFD) approach, a framework that involves customer expectation in decision-making is proposed for maintenance (inspection) prioritization, rehabilitation, and   10 replacement scenarios (MRR). A case study has been done using data available online from Johnson Bridge in Victoria, BC.  Chapter 5: Contains a study that can be used to predict customer response using observed parameters of interest to the customers thereby achieving objective 3 (Section 1.5). The method has been implemented by means of a hidden Markov model (HMM) and demonstrated using the 2005 customer satisfaction survey from the California Department of Transportation. Chapter 6: Contains conclusions made from the study presented in Chapters 3-5 and includes recommendations for further research Appendices A & B present worked examples related to HER framework and QFD implementation, respectively. Appendix C provides a Microsoft Visual Basic Application (VBA) code for implementing the hidden Markov model within QFD using a spreadsheet.     11          Literature Review Introduction Bridge Management System (BMS) Uncertainty related to BMS Decision Making in Bridge Maintenance Quality Function Deployment  Condition Assessment using HER Framework QFD Bridge Inspection Prioritization QFD Bridge Replacement/Rehabilitation  QFD Customer Requirement Prediction using Hidden Markov Model (HMM) FOR  ALL OBJECTIVES OBJECTIVE  1 OBJECTIVE  2/3 OBJECTIVE  4 FOR ALL OBJECTIVES CHAPTER 1 CHAPTER  2 CHAPTER  3 CHAPTER  4 CHAPTER  5 Conclusions & Recommendations CHAPTER 6 Figure 1-2 Thesis Organization   12 Chapter  2: Literature Review 2.1 Maintenance History Although the Romans were not the first to build bridges, they are recognized for having understood deterioration and maintenance concepts of bridges. Investigation into timber bridges built by the Romans revealed that the wood was preserved by soaking in oil and resin as protection against dry rot and coating them with alum for fire proofing (Chiu 2010).  This demonstrates that the concepts of bridge maintenance were envisioned thousands of years ago. In the current century, concrete and steel have been adopted as common materials for bridge construction and are subject to aging and deterioration similar to other materials. The amount of deterioration can be determined by means of an inspection and the importance of inspecting even a single component is well understood by the history of bridge failures. Specific component failures have led to collapse of major bridges. A few examples are (Little 2002): • Mianus River Bridge in Connecticut in 1983 (failure of a rusted hangar pin)  • Hatchie River in Tennessee in 1989 (failure of two columns)  • Schoharie Creek Bridge in New York  in 1987 (scouring of piers)  More recently, investigation into the I-35 bridge collapse over Mississippi River in Minnesota has been attributed to bowed gusset plates reaching their yield limit (Hao 2010). The bowing of the plates were noticed during previous inspection. This emphasizes the need for proper interpretation of inspected data and appropriate remedial measures. In contrast to specific component failures, exogenous events such as earthquakes have caused either minor damage, major damage, or collapse of bridges (e.g., Fenves and Ellery 1998; Chang et al. 2000; Tesfamariam and Modirzadeh 2009).    13 Recent history of bridge maintenance began during the years 1930-1940 when detailed inspection programs were developed by the Federal Highway Administration (FHWA). In December 1967, a major bridge collapse on Ohio River killed about 46 passengers prompting the US to evaluate and update highway safety and inspection procedures. This resulted in a memorandum that directed a review and inventory of all highway structures, inspection during a subsequent 5-year period (2 years for important structures) and the use of qualified persons for inspection. In order to make this program permanent, the National Highway Bridge Inspection program with recommendations was established in Federal Highway Act of 1968. Following this, American Association of State Highway and Transportation Officials (AASHTO) and the FHWA developed maintenance manuals for bridges. The National Bridge Inspection Standards (NBIS) was introduced in 1971 as a result in order to provide uniform maintenance criteria for the various bridge agencies. Subsequent legislation in 1978 established replacement and rehabilitation programs for structurally deficient/ obsolescent/ deteriorated bridges. In 1991, the Intermodal Surface Transportation Efficiency Act (ISTEA) mandated each state in the US to develop a Bridge Management System (BMS). 2.2 Bridge Management Systems (BMS) 2.2.1 General The innovations in computing along with the introduction of asset management concepts in bridge maintenance had prompted bridge stakeholders in the US to adopt a computerized Bridge Management System (BMS). BMSs are decision support tools developed to assist in determining how and when to make bridge investments that will improve safety and preserve existing infrastructure (FHWA 1999). In doing so, from an engineering standpoint, the current bridge condition state is mostly relied upon by effective inspection practices. The national co-operative   14 highway research program report 375 (Patidar et al. 2007) provides exhaustive information on inspection practices in the US and selected foreign countries. Furthermore, most BMS include life cycle costing (LCC) concept which is defined as a decision making approach that is based on the total cost accrued over the entire life of a bridge extending from its construction to its replacement or final demolition (Morcous 2002a).  2.2.2 Condition Assessment of Bridges A bridge management system, in general, facilitates interconnecting three scenarios: evaluation, prediction, and decision-making (Figure 2-1) and are defined as follows: Evaluation: Condition evaluation involves collecting direct observations (visual inspections or using devices) in order to obtain possibilities of failure - or distress indicators. The distress indicators then need to be quantified and translated into a failure probability thereby providing an assessment of bridge condition for further action. The condition is evaluated by assigning a rating that is dependent on the damage state of the bridge component.  PredictionDecision-making: Based on the type of maintenance problem, this can be a prioritization or scenario-selection problem. For example, if maintenance needs are to be prioritized based on cost, a cost-prioritization can be carried out; scenarios to replace, rehabilitate, retire, etc., a bridge may require decision scenarios for evaluating options.   : Normally, a probabilistic analysis is carried out to predict how the state of the evaluated condition changes with time. For example, for a component with low damage rating, this process could be used to predict after how much time a higher damage state is reached, or in the case of retrofit, the reverse is possible, i.e., to evaluate after how long damages can occur.    15  BMS can aid in funding allocations. The decision-making in most BMS is done at two separate levels - Network Level and Project Level. Network level consists of an inventory of bridges and decision-making is carried out for prioritizing funding allocations. Project level is defined as the level where each bridge repair strategies are determined at the component level. In the following paragraphs, a concise review of BMS in the US, Canada, Europe and internationally is provided. 2.2.3 Pontis® - The United States BMS Although most bridge management agencies have developed effective inspection practices through quality assurance/control (QA/QC) programs, in the US, the National Bridge Inspection Standards (NBIS) was established in 1971 to provide guidelines and uniform criteria for various highway agencies. The standards are based on the AASHTO manual for maintenance inspection of bridges. The objective of NBIS is to specify inspection requirements (White et al. 1992). These initiatives have led to the development of various technologies and techniques during the last few years to inspect/monitor bridge systems. The NBIS was introduced as a result of the Federal Highway Act of 1968 and consists of a component recording system which is still in practice. The 1991 Intermodal Surface Transportation Efficiency Act (ISTEA) mandated each state to develop a Bridge Management System (BMS). This led to the use of Pontis® a federally advocated, computer-based BMS model and allowed more details of individual bridge elements (AASHTO 1997). Pontis® is the most commonly adopted BMS with relevant modifications to suit each state's bridge inventory type. As per the Bureau of Transportation Statistics, there are 600,000 bridges in US. Nearly 40% of those bridges are considered deficient and are eligible for funding under the Highway Bridge Replacement and Rehabilitation Program (Frangopol 2002).    16 Data Collection and Management Analysis Program Formulation and Planning           Needs      Predictions    Options     Database                  Figure 2-1 Components of a BMS4  With most of those bridges being managed by Pontis®, this is recognized worldwide as an effective BMS with a few other countries in Europe having adopted Pontis® with modifications to suit their inventory. Pontis® was adopted by AASHTO as an AASHTOware product (meaning that Pontis® is part of AASHTO's family of software products) in 1994 and by individual states at various times between the years 1995-2005.  Pontis® uses a National Bridge Inventory (NBI) rating evaluated for a larger group of bridge elements, such as deck, superstructure, substructure, and culverts. Pontis® also requires a more refined condition rating by inspecting the bridge at an element level what are known as AASHTO Commonly Recognized (CoRe) elements (AASHTO 1997). The element level inspection is quantified by three to five condition states where the lower numerical value represents low damage and the higher value represents high damage. Table 2-1 shows the bridge components (elements) referred from the Colorado Department of                                                  4 http://www.fhwa.dot.gov/publications/publicroads/97july/ndejuly.cfm     17 Transportation (CDOT) Bridge Inspection Guide (CDOT 1998). Each element inspection is quantified by three to five condition states where condition state 1 represents good (low damage) Table 2-1 Colorado Department of Transportation (CDOT) Pontis® Elements and 5 represents bad (deteriorated) state. The collected inspection data (both NBI data and detailed element-level) is managed in Pontis® using the inspection module. Once both NBI and Pontis® element level inspections are imported, the AASHTO CoRe element codes can be converted to NBI condition codes using a translator. A sufficiency rating (SR) is then calculated based on Structure Evaluation Rating, Deck Geometry Rating, Vertical and Horizontal Rating and Structurally Deficient or Functionally Obsolete status generated by the program. The SR is represented as a percentage where 100% represents a sufficient bridge and 0% represents a deficient bridge. Two distinct maintenance actions are identified in Pontis® - preservation actions and functional improvements (NDOT 2009). Preservation actions seek to maintain or restore the physical condition of elements by carrying out maintenance, repair, rehabilitation or replacement of elements based on the objective of minimizing costs. Improvement actions are intended to Designation Material/Description Deck Concrete, Steel, Composite, Timber, Railroad Deck Slab Concrete Slab Super Structure Concrete, Steel, Timber, Other (Masonry) Substructure Concrete, Steel, Timber, Other (Masonry) WingWalls Slope Protection, Berms, etc. Approach Slab Concrete Bearings Elastomeric, Moveable, Fixed Joints Expansion, Seal, Elastomeric, Construction Culverts Steel, Concrete, Timber, Other Sidewalks Metal , Concrete, Timber Coatings Substructure and Superstructure Tunnel Lining Concrete Lined , Shotcrete Lined, Unlined Channel/RWA/General Channel, Bank, Debris, Waterway Adequacy, Approach Roadway Alignment, General Remarks Railing Concrete, Timber, Metal, Misc Flag/Pole Sign Attachment to Bridge   18 improve the structure to satisfy the current and future functional demands such as bridge widening, raising the bridge, strengthening and replacement. Improvement actions are based on policy standards (e.g., lane and shoulder widths, vertical and horizontal clearances, unit costs and benefits supplied by the user). Pontis® can evaluate scenarios among a network of bridges and rank them for further detailed action in a Project Level Analysis. The goal in network analysis is to evaluate alternatives by maximizing benefits with limited costs. The alternatives evaluated are preservation, preservation plus improvement, replacement and user-defined projects. The results of a network-level analysis serve as a good starting point for the project development and programming process. The deterioration modeling required for evaluating future condition for performance and cost analysis is performed using Markovian deterioration process. The Markovian process can handle uncertainties in the deterioration process. However, no uncertainties are considered within the condition assessment process in Pontis which is input to the predictive modeling and analysis. 2.2.4 BMS in Canada Canadian bridge agencies operate at three different levels (a) National by Transport Canada (b) Provincial/ Territorial by the Ministries of Transport, and (c) agencies at the municipal or local level (Patidar et al. 2007). Therefore, bridges in Canada are maintained at three management levels depending on the authoritative agency of the bridge. As such, every agency has its own BMS, although the concepts of maintenance are the same. However, unlike Pontis®, there is no such BMS at the National or Federal Level for the various agency levels to adopt. A comprehensive review of BMS in Canada is provided by Hammad et al. (2007) and Yan (2008). In addition, a review was done of bridge inspection guidelines in maintenance manuals of British Columbia, Alberta and Ontario. Currently no computerized BMS exists for Saskatchewan, New   19 Brunswick and Newfoundland. An implementation of computerized BMS is in progress for Prince Edward Island. Apart from these provinces, British Columbia, Alberta, Ontario and Quebec all have computerized BMS with the latter two based on Pontis® but with significant improvements to suit the agency's needs. Most of these BMS have standard features such as storage of inventory, inspection data, prediction tools, cost estimates, etc. The differences arise in condition rating system and with some BMS having additional modules for performance or cost analysis. The features of Canadian BMSs are summarized in Table 2-2..    Table 2-2 Summary of Canadian Provincial BMS Features Province BMS Condition Rating Limitations or Distinguishing Features British Columbia BMIS 5 Map-based interface for recording inspection data on laptops For each component in each condition state a percentage of inspection records is provided No module for budget forecasting and what-if scenarios Alberta BIMS 9, N, X Various Modules for: Condition State:  Superstructure, Paint Functionality: Strength, Bridge Width, Bridge Rail, Vertical Clearance Results from above Modules used in Substructure and Replacement Modules Cost Estimate and Timing of each activity is generated Saskatchewan N.A 4 *No Computerized BMS* Manitoba Pontis® 5 Pontis® is used for Manitoba Bridges. Refer Section 2.2.1 Ontario OBMS 4 Knowledge based model for choosing rehabilitation scenarios based on MTO rehabilitation manual Comprehensive cost database with tender items covering 12 Ontario Districts Quebec QBMS 5 Similar to OBMS, but in addition to deterioration and cost model has a treatment model that specifies list of treatments for an inspected element Inspection is stored in time-series; each inspection for a given element has a list of condition and maintenance needs during the past 3 years  Element alternatives and Project alternatives are generated by performing life-cycle cost analysis for either the inspected element or set of elements respectively New Brunswick N.A N.A *No Computerized BMS* Nova Scotia NSBMS 4 Similar to OBMS with modifications such as: Record defect extent (no. of defect) in addition to severity during inspection Record performance deficiencies (such as excessive deflection) Element alternatives generated as well as project alternatives for 1-5 yrs or 6-10 yrs period Prince Edward Island PEIBMS 4 *Implementation of Computerized BMS in Progress* Newfoundland N.A N.A *No Computerized BMS*   20 2.2.5 BMS in Australia and New Zealand In Australia, the states of New South Wales and Victoria have adopted Pontis® with minor modifications to suit their inventory. The only state where there has been advancement in BMS is Queensland and the initial Bridge Information System (BIS) was upgraded in 1998 to Bridge Asset Management System (BAMS). More recently, in 2004 a more advanced BMS called WHICHBRIDGE was adopted that can facilitate risk management based on probability of failure along with cost estimates for maintenance. Otherwise, there has been no standardized BMS in either Australia or New Zealand and agencies depend on inspection guidelines provided by their own bridge experts for maintenance and rehabilitation (Lee 2007).  2.2.6 Japanese Bridge Management System (JBMS) JBMS facilitates maintenance of concrete bridges in Japan. JBMS stores a large number of technical specifications, inspection and other data related to bridge maintenance. Unlike Pontis®, which operates at a project level and network level, JBMS evaluates the condition of each element (component) of the bridge at project level only. Current visual inspection results along with technical specification data are used to evaluate present performance of the bridge. The evaluation is done using a program called Bridge Expert Rating System (BREX) which outputs soundness of the load carrying capacity or durability on a scale of 0-100. BREX uses fuzzy and crisp rules constructed using hierarchical neural networks for dealing with uncertainty. The program has prediction deterioration curves that are soundness vs. deterioration curves established using experimental work. Using the current performance results and the experimental deterioration curves, remaining life of the bridge is estimated along with a rehabilitation strategy. All this is done at the bridge level and hence, the system cannot keep track of a network of bridges and allocate funds among the bridge inventory (Bakht and Mutsuyoshi 2005).   21 2.2.7 South African Bridge Management System The South African Roads Agency Limited (SANRAL) had a condition-based bridge management system for 20 years that included both roads and bridges. Since bridges deteriorated at a slower rate compared to roads, most bridge projects got delayed. SANRAL therefore decided to go with a defects-based BMS as that provided a better prioritization model for identifying and prioritizing bridges in need of repair. The defects based BMS is called STRUMAN and has four modules - inventory, inspection, condition and budget. In the inspection module, the worst defect per element is rated for Degree (D), Extent (E), Relevancy (R), and Urgency (U) of repair on a scale of 0 to 4.  With the defects-based BMS, the inspector does not have to rate every element, but only rate defects along with their effect on the element under consideration. In the condition module, three indices are evaluated - a condition index (for ranking the bridges requiring repairs), priority index (priority among overall bridge elements) and functional index (importance depending on location of bridge). Prioritization along with cost estimates is done depending on the need for rehabilitation and repair (Kruger and Ronny 2005). 2.2.8 European Bridge Management System  Although current structural design in Europe has been made consistent by the advent of Eurocodes for design, there seems to be variation between countries in Europe regarding bridge maintenance activities. The current European Union consisting of 27 member states has recognized this in the past and state-of-the art research has been conducted by the way of framework programs (FPs). Currently there is a seventh framework program (FP7) in place to support decision-making for roadways at the European level. Previous frameworks FP4, 5, and 6 have contributed significantly in initiating or improving BMS in Europe (Helmerich et al. 2008).   22 Various tools used by some agencies in Europe are provided in Table 2-3. Some of the research done as part of the FPs is: • Bridge Management in Europe (FP4):  A project for sharing best practices in Bridge Management in Europe (abbreviated as BRIME) was initiated in the year 1998.  At the time, the study focused on eight countries covering France, Germany, the United Kingdom, Norway, Slovenia, Spain, Denmark, and Finland. Six among these used a computerized BMS. • European Co-operation in the Field of Scientific and Technical Research (COST) 345 (FP4): research in detailed procedures for condition assessment and inspection of highway structures. • LIFECON (FP5): The objective was to develop and validate an open and generic European model of integrated and predictive life-cycle maintenance for all civil infrastructures. The research has led to the development of Lifecon Life-cycle Management System (LMS). To summarize, the concepts are similar for various BMS available, however the technical terms differ in the rating systems used for elements inspection and the way uncertainty is handled in the management system. The process of condition assessment, prediction of deterioration, and decision-making all involve uncertainty. Few practical BMS systems adopt frameworks for dealing with uncertainty, and there has been some research in this direction. However, the uncertainty methods may not be effective enough given that bridge inspection is still relied on visual inspection results that involve subjective judgment that leads to uncertainty.  While the visual inspection could be made more effective using experienced bridge inspectors, the presence of such expertise may not alleviate uncertainty. For example, if the bridge component is not visible for inspection or if the weather conditions are not favorable (such as rain, snow, wind, etc.), the inspection reporting may not be accurate. Likewise, similar damage inspected by   23 Table 2-3 Summary of European BMS Features Country BMS Condition Rating Limitations or Distinguishing Features Sweden BaTMan 0-4 • Condition Class (CC) is used rather than state. CC is defined as the extent to which functional properties are satisfied. OCC is defined as overall condition class for the bridge • No deterioration models; physical and functional conditions are based on inspectors judgement. For example, comparison between previous inspection state and current state is made to identify deterioration process Denmark DANBRO 0-6 • Condition rating is identified for components and overall bridge rating is based on the premise that overall rating cannot be higher than maximum rating of individual component or less than that for main components such as pier, girder, etc • No deterioration model; evaluation based on inspector's judgement Swiss KUBA 1-5 • Condition assessment of elements is refined by dividing them into segments • Markov chains are used to forecast element deterioration • Element preservation and optimal costs are generated. Germany SIB-Bauwerke 1-1.4 1.5-1.9 2-2.4 2.5-2.9 3-3.4 3.5-4.0 • Each defect is weighted with regards to structural safety (stability) 'S' traffic safety 'V', and durability 'D'. This scheme is applied both to either an element or the whole bridge • A defect catalog in the system tries to cover all possible defects. Overall the conditions of bridges are stored. No cost analysis is carried out • 3 year interval for general inspection and 6 year interval for major inspections Finland FBMS 0-4 • results from network level are used to evaluate individual bridge condition • damages are grouped into surface, structural and water leakage. Interdependency between the groups is considered • cost minimization is done based on repair costs and bridge user costs  different inspectors with varying levels of experience could result in different ratings. Therefore, the confidence level of the information obtained could vary thereby exhibiting uncertain characteristics. 2.3 Uncertainty Handling in Bridge Maintenance  2.3.1 Uncertainty Sources & Analysis Techniques Uncertainty is broadly classified into two types - Aleatory and Epistemic Uncertainty. Aleatory uncertainty is a variability which is inherent in the natural phenomenon or a process. This is also   24 termed as irreducible uncertainty as the variability is inherent in the system and cannot be reduced. For example, the measurements of similar sized members on a steel bridge may vary because of variability in the manufacturing process. This would have nothing to do with the inspection of the bridge. Epistemic uncertainty occurs due to lack of information in the system that leads to a deficiency in selecting the best option given a set of possibilities (Nikolaidis et al. 2005). The lack of information can occur due to, vagueness, ambiguity (causing conflict and nonspecificity, etc). (Tesfamariam et al. 2010). Since the lack of information can be investigated and reduced to provide better outcomes, this is also termed as reducible uncertainty. For example, a bridge component inspected by different inspectors could result in varying damage information. The damage information reported by experts in linguistic terms could be vague or conflicting when there is multiple experts’ opinion. Such recorded information when used to make a decision can lead to errors since the decision would be made under uncertainty. For the purposes of the proposed research, epistemic uncertainty holds relevance and the methods for handling this type of uncertainty are discussed in the following sections. The effectiveness of infrastructure management either in terms of performance or cost estimates would depend on the accuracy of future information predicted by the deterioration model. Furthermore, deterioration model would require input regarding current condition of the structure that needs to be estimated precisely. Infrastructure deterioration is stochastic in nature and modeling is a complex process involving highly uncertain parameters (Gao and Zhang 2011). Uncertainty in infrastructure management can arise through the following sources: • measurement (inspection) and condition assessment • deterioration due to inherent randomness in the system   25 • condition evaluation and deterioration model (e.g.,  quality is a parameter which is hard to quantify, therefore  a marked deviation between the actual structure and what is modeled can be expected) Soft computing methods that employ data fusion techniques have been developed for addressing the requirements of combining such data (e.g. Bolar et al. 2012a). Data fusion is the synergistic aggregation of complementary and/or redundant observations and measurements and is useful for objective aggregation that is reproducible and interpretable. A comprehensive review of soft computing applications in infrastructure management is provided by Flintsch and Chen (2004). However, these techniques do not necessarily account for confirmatory and/or contradictory information rationally. Consequently, there exists the possibility that condition ratings are highly dependent on the underlying assumptions. Epistemic uncertainty arises due to lack of information such as incomplete information or ignorance about the system under consideration. Traditionally treated as a random variable using subjective probability distributions, this can lead to erroneous results. For this reason epistemic uncertainties have been best handled using theories such as fuzzy set theory, possibility theory, evidence theory, etc. While some of these methods can only deal with epistemic uncertainty, methods such as evidence theory can handle both epistemic and aleatory uncertainty in one framework.  In evidence theory there are two complementary measures of uncertainty – belief and plausibility that represent lower and upper bounds of an interval-based probability. Therefore, this is a marked distinction compared to traditional probability where one measure is used compared to two measures in evidence theory. The evidence theory is also known as the Dempster-Shafer   26 theory of evidence where probabilities are assigned to sets instead of mutually exclusive singletons.  2.3.2 Soft Computing Methods for Bridge Condition Assessment Multi-Criteria Decision Making (MCDM) is a branch of decision analysis wherein a set of alternatives are evaluated using a set of decision criteria. If the alternatives are known before the solution process and the intent is to rank the alternatives, the MCDM is termed as Multi-Attribute Decision Making (MADM). If the alternatives are not known and can be determined using a mathematical model, the term Multi-Objective Decision Making (MODM) is used. Infrastructure condition assessment is normally represented as a MCDM problem as multiple criteria or attributes exist and the alternatives are among the structure inventory that is known. Furthermore, the attributes can be conflicting with each other. If the set of attributes is large, they can be arranged in a hierarchical manner such as parent attribute, followed by sub-attributes (Triantaphyllou et al. 1998). Among the techniques to solve MADM problems, widely adopted is the Analytical Hierarchy Process (AHP) developed by Saaty in the 1970s. AHP has been used along with various techniques to handle uncertainty such as deterministic, stochastic and fuzzy methods (e.g. Tesfamariam and Sadiq 2006). Among the bridge condition assessment literature reviewed, AHP has been adopted by most researchers along with uncertainty handling techniques such as fuzzy sets. AHP involves constructing a decision-making problem in various hierarchies as goal, criteria, sub-criteria, and decision alternatives. The AHP technique performs pairwise comparisons to measure the relative importance of elements at each level of the hierarchy and evaluates alternatives at the lowest level of the hierarchy in order to make the best decision among multiple alternatives. AHP provides decision makers with a way to transform subjective judgments into objective measures (Sipahi and Timor 2010). Various other techniques   27 have been used by researchers for handling uncertainty and representing knowledge in either damage evaluation or condition assessment of bridges Table 2-4 provides a summary of these techniques. Table 2-4 Soft Computing Methods in Bridge Condition Assessment Author Year Evaluation Type Note 1 Knowledge Representation Uncertainty Representation Chiang et al. 2000 Fuzzy Petri Net Based Expert System D Hierarchical Fuzzy Petri Nets Fuzzy Truth Value Liang et al. 2001 Multiple Layer Fuzzy  D Multiple Layer Fuzzy None Zhao and Chen  2001 Fuzzy Inference System D Modified Mountain Clustering Method (MMM) None Lin et al. 2002 Neural Network Based  D Neural Networks None Estes and  Frangopol 2003 Updating Existing Visual Insp.Results R Bayesian Updating None Kei Kawamura and Miyamoto 2003 Neuro-fuzzy hybrid system D Neural Network None Sasmal et al. 2006 Fuzzy Logic Based Condition Rating C MADM model Fuzzy Logic Wang and Elhag 2006 Fuzzy TOPSIS method R Alpha Sets - Non Linear Programming (NLP) None Sasmal and Ramanjaneyulu 2008 Fuzzy based analytic hierarchy approach C Analytic Hierarchy Process (AHP) using MADM model Optimistic fuzzy membership function Wang and Elhag 2008 Evidential Reasoning  C Recursive Evidential Reasoning  Normalization Note 1: Assessment Type; D=Damage; R = Risk; C = Condition Assessment  Examples of fuzzy sets and AHP in bridge condition assessment are: Multiple Layer Fuzzy Evaluation (Liang 2001a): This study involved using a multiple layer fuzzy model for evaluating the damage stage of existing reinforced concrete bridges. The major items that influence strength and rigidity of a bridge such as girder, deck, pier and their components were assigned a rating grade I through V (no damage to severe damage). Fuzzy set was adopted as the analysis method and fuzzy membership was partitioned into Grade I-V.  Single layer fuzzy synthetic evaluation was first done followed by multiple layers in order to increase reliability.     28 Fuzzy Based AHP Techniques (Sasmal and Ramanjaneyulu 2008): Here, fuzzy based AHP approach has been adopted for priority ranking and condition evaluation of concrete bridges. Fuzzy logic technique is used to take care of the uncertainties including imprecision from bridge inspector observations. For priority ranking, comparison matrices are adopted for identifying relative importance of items. Fuzzy numbers and fuzzy membership functions are then generated to obtain fuzzy synthetic matrix. A condition index of the items is then obtained and prioritized. The overall best bridge condition rating was obtained using fuzzy weighted average (FWA) and fuzzy resolution identification technique.   2.3.3 Dempster-Shafer Theory of Evidence The DST is a powerful tool to address epistemic uncertainty (ignorance). The DST was first proposed by Dempster (1967) and subsequently extended by Shafer (1976). In DST, a finite nonempty set of mutually exclusive alternatives (condition states) is called the frame of discernment, denoted by Θ, and has 2Θ subsets in the domain. This frame of discernment contains every possible hypothesis in the power set.  The basic probability assignment (BPA), an important concept in DST, reflects a degree of belief in a hypothesis or the degree to which the evidence supports the hypothesis. BPA has the following properties 1)( =∑ ΨΘ⊆Ψm ; 0)( =φm ; ,1)(0 ≤Ψ≤ m  for all Θ⊆Ψ      (2-1) where )(Ψm  represents the direct support of evidence on Ψ, i.e., indicates that portion of the total belief exactly committed to hypothesis Ψ given a body of evidence. BPA  can be assigned to every subset Ψ (where Ψ ⊆ Θ)with interval value of [0, 1],. If the existing evidence cannot differentiate between two hypotheses, say, Ci and Cj, a BPA could be assigned to the interval i.e. subset that consists both of these hypotheses, denoted by m({Ci , Cj}). m(Φ) represents mass of   29 the null (empty) set. The quantity m(Θ) is a measure of that portion of the total belief that remains unassigned after commitment of belief to all subsets of Θ. If m(Ψ) = s, and no BPA is assigned to other subsets of Θ, then m(Θ) = 1 - s. Thus, the remaining BPA is assigned to Θ itself, but not to the negation of a subset Ψ. This value of BPA m(Θ) represents ignorance (Sentz 2002). Refer Appendix A1for example calculations. 2.3.4 Dempster-Shafer (DS) rule of combination  The DS rule of combination, also sometimes referred to as the orthogonal sum of evidence, can be used to aggregate multiple sources information. Assume two bodies of evidence exist in Θ, i.e., two basic probability assignments m1(Ψ) and m2(Ψ) to a subset Ψ ⊆ Θ. The combined probability assignment, m12(Ψ), based on the DS rule of combination is,  Φ≠Ψ−∑Φ=Ψ=Ψ⊕Ψ=ΨΘ⊆∀Ψ=∩ when1)()(when0)()()(,,212112KBmAmmmmBABA      (2-2) where ∑Θ⊆∀Φ=∩=BABABmAmK,,21 )()( . The combined mass probability assignment, m12(Ψ), for a subset Ψ is computed from m1 and m2 by adding all products of the form “m1(A) • m2(B)”, where A and B are the subsets and their intersection is always Ψ. The conflict between subsets A and B is represented by factor K, where the intersection of A and B (i.e., A ∩ B = Φ) is an empty or void set.  The commutative property of the DS rule of combination ensures that the rule yields the same value regardless of the order in which the two bodies of evidence are combined (Sadiq et al.   30 2006). Therefore, the DS rule of combination can be generalized to more than two bodies of evidence as,  MM mmmm ⊕⊕⊕= 21,...,2,1                           (2-3) The direct use of the combination rule in Equation (2-3) will result in an exponential increase in the computational complexity. Generally, the DS rule of combination is used recursively to avoid this complexity. In this study, the recursive DS algorithm is applied to the hierarchical framework. Combined evidence, )(iI ke , based on the combination i parameters that contribute to the kth attribute is obtained by applying the recursive DS rule of combination as follows, kikkkiI Lieeee k ...,,2,1...21)( =⊕⊕=        (2-4) Assume nkHiIm )( is a BPA of a subset (singleton) Hn ⊆ H, which is confirmed by combined evidence, )(iI ke , and can be written as, },,2,1,){()()()( NnmHemnkk HiIniI ==        (2-5) In the above equation, the letter “I” denotes that )(iI ke is not an observable evidence but rather a result of the combination of observed bodies of evidence. For instance, a combination of two parameters, i.e., i = 2, would be, 21)2( kkI eee k ⊕=           (2-6) By applying DS rule of combination for two parameters, a conjunctive logic AND operator (estimated by a product of two probabilities) is employed. The basic probability assignments to condition states Hn, and H with respect to )2(kIe can be derived as, nkHIm )2( = )()(}{1,2,2,1,2,1,)2()2(HkHkHkHkHkHkIIn mmmmmmKemHnnnnkk++=      (2-7)   31 HI km )2( =HkHkIImmKemHkk2,1,)2()2( )(}{=     where 11 ,12,1,)2( )1(−= ≠=∑ ∑−=NsNslllkskI mmK k .        (2-8) It is evident that 0)2( =ΨkIm , for all other subsets (Ψ) except when Ψ = Hn (n = 1, 2,…, N) or H. The DS rule of combination can be generalized for the aggregation of multiple parameters as expressed earlier in. The same result is obtained regardless of the order in which the evidence is combined because of the associative nature of DS rule of combination. For computational simplicity, recursively, we combine one parameter at a time using the following formulae. nkHjIm )1( + = )()(}{)(1,1,)(1,)()1()1(HjIHjkHjkHjIHjkHjIjIjInknnknnkkkmmmmmmKemH+++++++=    (2-9) HjI km )1( + =HjkHjIjIjImmKemHkkk1,)()1()1( )(}{+++=        (2-10) where, 11 ,11,)()1( )1(−= ≠=++ ∑ ∑−=NsNsllljksjIjI mmK kk ; j = 1, 2, …, Lk – 1    (2-11) Refer Appendix A2 for example calculations on D-S rule of combination. 2.3.5 Yager Modified Dempster-Shafer (DS) rule of combination A recursive combination technique similar to the previous DS rule of combination is applied in the current study. The only difference in Yager rule is the elimination of normalization by non-conflicting evidence. The conflicting evidence represented by the factor 'K' is shifted to ignorance during data combination (Tesfamariam et al. 2010). The basic probability assignments to Hn, and H with respect to )2(kIe can be derived as, nkHIm )2( = )()(}{1,2,2,1,2,1,)2(HkHkHkHkHkHkIn mmmmmmemHnnnnk++=       (2-12)   32 HI km )2( =HkHkIImmKemHkk2,1,)2()2( )(}{+=         (2-13) where 11 ,12,1,)2( )1(−= ≠=∑ ∑−=NsNslllkskI mmK k .        (2-14) Similar to the DS rule of combination, the above equations can be generalized for the aggregation of multiple parameters: nkHjIm )1( + = )()(}{)(1,1,)(1,)()1(HjIHjkHjkHjIHjkHjIjInknnknnkkmmmmmmemH++++++=     (2-15) HjI km )1( + =HjkHjIjIjImmKemHkkk1,)()1()1( )(}{++++=        (2-16) where 11 ,11,)()1( )1(−= ≠=++ ∑ ∑−=NsNsllljksjIjI mmK kk ; j = 1, 2, …, Lk – 1    (2-17) 2.4 Decision-Making in Bridge Maintenance BMS aims prioritization and decision making for funding allocations among an inventory of bridges (also known as network level analysis) and hence provides a starting point for examining bridge repair strategies at the component level (also known as project level analysis). However, limited literature is published, where input from the bridge-user and stakeholders is incorporated in the bridge maintenance decision-making process (e.g. Bolar et al. 2012b; Malekly et al. 2010; Junhai et al. 2007; Lair et al. 2004; Sarja 2004; Söderqvist and Vesikari 2003). This process can be facilitated by adopting a widely used method in manufacturing, called Quality Function Deployment (QFD).  With condition evaluation results, a decision-maker has to choose mostly between ‘do-nothing’, ‘rehabilitate’ or ‘replace’ options. With consumers such as bridge users becoming more involved in sustainability issues, including them in the decision-making process would prove valuable to   33 all the stakeholders involved. A decision to either replace or rehabilitate a bridge can affect individuals and departments in various ways. In this context, a bridge user is defined as anyone that is affected by modifications to the bridge. For example, a business located close to such a bridge might be affected by traffic volumes and so would be fire agencies, etc. The input of all these can affect decision making and including them in the process would be relevant. The primary input in the QFD process is customer requirements that are termed as ‘WHATs’ and the means of achieving those customer requirements are termed as HOWs. The WHATs are first prioritized and then two sets of matrices are generated, one relating the WHATs to the HOWs and another identifying the correlation between each HOWs. Using the WHATs and relationship matrix, absolute weights for each HOW are generated and can be ranked for decision-making. The correlation matrix helps identify strongly correlated (either positively or negatively) HOWs. These QFD concepts are depicted in Figure 2-2. The actual QFD process is conducted in what looks like a house and is accordingly called the ‘House of Quality’ in QFD (Figure 2-3).  The application of QFD for management of bridges is a relatively new concept. Only three references closely related to QFD for bridge design or maintenance are: • Junhai et al. (2007) report that portion of bridge lifecycle design in China is based on QFD. • Malekly et al. (2010) have used QFD in evaluating the conceptual bridge design.  • The European Life-Cycle Management System (LMS) tool LIFECON extensively adopts QFD (Söderqvist and Vesikari 2003). 2.5 Quality Function Deployment In the late 1960s, Mitsubishi Heavy Industries was involved in construction of massive super tanker cargo ships at Shipyards in Kobe, Japan (Guinta & Praizler 1993). Each cargo ship was built differently as each customer purchasing the super tanker had specific cargo holding requirements,   34 thereby making this an extremely challenging ordeal.  The Japanese government at the request of Mitsubishi contacted universities to come up with a logistic where each step of the construction process was linked to a specific customer requirement. This led to the development of what is today known as Quality Function Deployment (QFD). During the same time period in the automotive industry, Toyota had issues with their small cars in the US as the public perceived them as cheaply built with doors rusting quickly. Toyota decided to adapt the new methodology from Mitsubishi and called in customer focus groups to find out about their doors from the customers. The outcome of the meeting included additional items the customer disliked such as the weight of the door  when parked downhill, number of window cranks to open the window, etc. Using QFD the company was able to capture the preferences of the customer and incorporate them in the engineering and manufacturing process. QFD proved successful to Toyota and they extended this system to design other parts of their cars. Today, QFD is extensively used in Toyota's designs and has been widely adopted not only by the manufacturing industry, but also among various other disciplines. Some areas where QFD has been applied extensively include, but are not limited to are aerospace (Kojima et al., 2007; Pica et al., 2008), defence (Stanfield and Cole, 2008; Kirpatrick et al., 2008; Bergman, 2008), public transportation (Hopwood II and Mazur, 2007), education (Chen et al., 2002, Chan et al., 2007; Prusak, 2007; Durán, 2007), lifecycle analysis (Nakamura, 2007; Cheema and Hussain, 2007), logistics (Crostack et al., 2007), software (Lamia, 1995) the process industry (Lager and Kjell, 2007), soil tillage (Milan et al., 2003), telecommunications (de Souza et al., 2007; Xiong and Xia, 2007), health care (Helper and Mazur, 2008), construction (Gargione, 1999; Cariaga et al., 2007), environmental requirements (Utne, 2009; Zhang et al., 1999; Mehta and Wang, 2001; Masui et al., 2003; Ernzer et al., 2003; Gray and Bizri, 2006). The extent of areas where QFD has been researched has become so exhaustive that Carnevalli et al. (2008) investigated the research done in QFD as a research topic itself. Sharma et al. (2008) and Chan et al. (2002) have published   35 comprehensive literature reviews on the topic. Recent applications of QFD in engineering include oil and gas (Yang et al., 2011) and drinking water quality management (Francisque et al., 2011)  2.5.1 The QFD Process A flow chart depicting the various steps involved in QFD is provided in Figure 2-2. The actual QFD process is shown in a typical HOQ in Figure 2-3, and various terms and their role in QFD is described below: House of Quality (HOQ): The HOQ (Figure 2-3) is a term associated with QFD which is a matrix that documents and establishes all the processes in implementing QFD as shown in Figure 2-3. The various terms are defined in relation to infrastructure maintenance as follows: WHATs: The primary input in the HOQ is a prioritized list of basic customer demands (requirements and needs) that are usually expressed in vague and imprecise terms (e.g., riding comfort on a bridge, environmentally friendly materials, etc.).  Each demand is documented as a WHAT and prioritized as represented by WHAT-1, …WHAT-n in Figure 2-2.  HOWs: Once the WHATs are generated, the means of achieving these WHATs is identified and termed as HOWs. Therefore, HOWs are the design (or technical or product) characteristics that serve to meet the WHATs (e.g., maintenance-aimed at no potholes on a bridge, green products or construction for customer requiring environmental compliance, etc.). For each WHAT, a corresponding HOW is identified as represented by HOW-1,…,HOW-n in Figure 2-2. Relationship matrix: Indicates how product characteristics or decisions affect the satisfaction of each customer need. It consists of relationships existing between each WHAT and each HOW attribute (i.e. WHAT vs. HOW as shown in Figure 2-2).       36                Figure 2-2 QFD Process Flowchart Relationship Prioritize Relationship WHATs Customer  Input WHAT-1 WHAT-n HOWs HOW-1 HOW-n Correlation Absolute Weights Ranking   37   Figure 2-3 House of Quality (HOQ) Absolute weights and ranking of HOWs: contains results of the prioritization of product characteristics to satisfy customer requirements. It represents the impact of each HOW attribute on the WHATs and is the final step before ranking of the weights for decision-making as shown in Figure 2-2. Correlation matrix: is the roof of the HOQ and represents the interdependencies among HOWs as shown in Figure 2-2. It can play an important role in deciding on the number of HOWs that directly affect the cost, prioritizing WHATs and HOWs.    38 2.5.2 Prioritization Techniques for QFD To satisfy customers, their needs must be prioritized, i.e., the level of relative importance to be attributed to the WHATs must be determined. Once WHATs are determined and prioritized, it is important to decide how to obtain the desired results, i.e., how to satisfy customers’ prioritized needs. Determination of HOWs implies translating customer needs expressed in subjective terms into requirements of a technical nature (e.g., increasing taxes, condition evaluation of bridge paint/coatings, inspect approach alignment, upgrade with environmentally friendly materials and/or construction). These characteristics are indeed a product or service description expressed in technical (i.e. infrastructure manager) language. It involves establishing a list showing the HOWs (at least one HOW for each WHAT). Product characteristics represent the quality offered (Qo) demonstrated through a product or service description provided in measurable terms and should directly affect customer perception of quality (Franceschini, 2002). However, before prioritizing HOWs, it is important to indicate how these characteristics affect the satisfaction of each WHAT. The HOQ relationship matrix must be completed using correlations defined between each WHAT and each HOW. Three elements determine the importance of HOWs: the importance of the WHATs to which the HOW is correlated, the level of correlation (e.g., weak, medium, strong), and the degree of difficulty its realization entails (Franceschini, 2002). In this study, three methods (explained in detail using examples in Appendix B) are used for the prioritization of HOWs attributes. The main difference between these methods lies in the way the cardinal relationship rij between the i-th WHAT attribute and the j-th HOW attribute is calculated:  i. Independent scoring method is the classical method of QFD (Akao, 1988). Cardinal relationships rij constituting the relationship matrix (Figure 2-3) are not normalized. This method presents a major drawback in certain cases. It can assign a weakly relative importance to some HOW attributes (e.g., traffic signs) that have a strong correlation   39 with some WHATs more important for the customer (e.g., pedestrian safety), and vice versa. It depends on the way the product characteristics (HOWs attributes) are defined, i.e., if they are subdivided into sub-characteristics or not. ii. Lyman’s normalization method (Lyman, 1990) tries to resolve the issues related to the independent scoring method by normalizing the coefficients rij in the relationship matrix (Figure 2-3); and iii. Wasserman’s normalization method (Wasserman, 1993) is an extension of Lyman’s method that considers interdependence between HOWs attributes, i.e., the matrix of correlation - the roof of the HOQ (Figure 2-3), in the normalization process. 2.5.3 Rating Systems for QFD Three distinct rating systems are adopted in the QFD process. The first rating normally referred as an importance rating involves prioritizing the WHATs in order to reflect the customer's opinions. The second is a measure of correlation between the WHATs and HOWs, and the third is a measure of inter-relationship between the HOWs.  Importance Rating Evaluating an importance rating involves prioritizing the WHATs in order to reflect the customer's opinions. For example, a bridge user may consider aesthetic value more important (and hence a higher rating) compared to economic considerations.   The original QFD scales for importance rating used Japanese symbols for Win (Circle with solid dot at the centre), Place (Empty Circle) and Show (Empty Triangle) from horse racing tracks, representing values of 9, 3 and 1. When QFD emerged in the United States, teams found no difference between representation using numerals or symbols and therefore numerals gained popularity. The Japanese QFD sometimes use a scale of 1-to-9 and other times a scale of 1-to-5 in all cases 1 representing low importance and 9 or 5 representing high importance. The Analytic Hierarchy Process (AHP) developed by Saaty (1988) is one of the methods that can be used to assign level of importance to the WHATs   40 (Francisque et al., 2011). Table 2-5 provides a scale to assign relative importance to customer requirements.  Table 2-5 Fundamental scale used to developing matrix for AHP (Saaty, 1988) Intensity of Importance Definition Explanation 1 Equal importance Two activities contribute equally to the objective 2 Weak ― 3 Moderate importance Experience and judgment slightly favor one activity over other 4 Moderate plus ― 5 Strong importance Experience and judgment strongly favor one activity over other 6 Strong plus ― 7 Very strong or demonstrated importance An activity is favored very strongly over another; its dominance demonstrated in practice 8 Very, very, strong ― 9 Extreme importance The evidence favoring one activity over another is of highest possible order of affirmation Relationship Matrix Ratings: Relationship matrix rating is a measure of correlation between the WHATs and HOWs i.e., the extent to which each of the HOWs could accomplish a WHAT. This is represented in the relationship matrix by comparing each WHAT on a pairwise basis to all the HOWs. For example, a single WHAT, say a bridge overlay condition is compared to all HOWsgenerated such as condition evaluation of bridge coatings, increase taxes, etc. Normally, a 0-to-5 rating is used where 0 represents no relationship and similar to importance ratings, 1 represents low and 5 represents high importance. Correlation Matrix Ratings: Each HOW is compared to all the remaining HOWs on a pairwise basis in order to identify positive or negative inter-relationships that usually represent trade-offs. Positive relationship is used to represent HOWs that support each other and negative relationship represents HOWs that are in conflict. For example, for a given structure, using a decorative paint or coating may correlate strongly with aesthetic value, but negatively with increased cost. These are shown in the roof of the House of Quality normally using positive or negative symbols with modifications to   41 show strong positive interrelationship (such as a circle around +) or strong negative relationships (ReVelle et al., 1998). Any negatively correlated items in the roof of the house of quality indicate items requiring improvement or even lead to research and development. The correlation matrix symbols used in various QFD studies are varied with each researcher using different symbols such as tick and check mark symbols, etc. In this study, these correlations are established on a 3-tier scale ranging from 0 to 1, where weak is 0.1, medium 0.3 and strong 0.9. 2.6 Predicting Customer Requirements A primary input to the QFD process is customer requirements that are normally based on surveys and questionnaire. However, these customer requirements are dynamic in the sense that depending on time and space the expectation could vary. For example, in a good economic condition if a customer is questioned about improving aesthetics on a bridge, the answer may be positive, but if the economic condition is bad a natural answer expected would be to "hold on" to that activity and perhaps prioritize among safety and other hazardous issues. Customer requirements can therefore change over time and keeping up with customer requirements can pose challenges. In order to keep up with changing requirements frequent and repeated customer surveys can be conducted, but they involve cost, time and effort in collecting the information and generating results. A hidden Markov model (HMM) can aid in the determination of future probabilities using currently available probabilities as "known parameters" and by modelling related time-dependent entities as hidden parameters. In the case of infrastructure, given the responses of infrastructure users as "known parameters" and related focus areas of interest to the customer as time-dependent parameters, future response of the customer can be predicted.     42 2.6.1 Hidden Markov Model in Civil Engineering Problems In general, the applications of Hidden Markov Model (HMM) can be widely found in electronics and telecommunication industry for image sequencing, recognition techniques, etc. (Rabiner 1989). However, not many applications are seen within the civil-structural engineering domain. In the structural health monitoring discipline, an application of HMM for damage accumulation and propagation was proposed by Rammohan and Taha (2005), whereas a model for pavement deterioration was proposed by Lethanh and Adey (2013).  In the transportation discipline, a recognition method for lane change intention was proposed by Xu et al. (2011); and for vehicle recognition using image processing by Shen & Bai (2007). In hydrological research, HMM was applied by Mallya et al. (2013) in their study focusing on drought characteristics. Condition-based maintenance of machines using HMM was studied by Bunks et al. (2000) and Yu (2012). 2.6.2 Dealing with Dynamic Customer Requirements in QFD Companies dealing with product development have adopted QFD in order to identify and address customer requirements. These customer needs can be termed dynamic as their needs can vary over time. Chong and Chen (2010) provided a review of the current state of research related to dynamic customer requirements. In conclusion of the review, there was a recommendation to develop solutions that could automatically handle dynamic customer requirements. Similar literature review was done by Sepideh and Aaghaie (2011), but focusing on the use of HMM alone. According to their findings, in customer relationship management (CRM), about 27% of published articles adopted HMM. A novel method integrating QFD with HMM was published by Shieh and Wu (2009) by adopting HMM to update QFD technical measures.  Application of HMM in the current study is based on the approach used by Shieh and Wu (2009), but has been extended for application to engineering, especially civil engineering problems where including   43 customer requirements is still at infancy and the customer expectations have a wide variety of parameters especially with more consciousness in sustainability issues.  2.7 Proposed Approach The objectives of this research are the following: • Objective 1: Condition Assessment  • Objective 2: QFD - Bridge Level for Inspection Prioritization • Objective 3: QFD - Inventory Level for Decision-Making between Rehabilitation and Replacement Schemes. • Objective 4: Prediction Scheme for Customer Requirements.  The proposed approach is illustrated in Figure 2-4. At the left & right of the figure are QFD house of qualities (HOQs) for inspection, replacement and rehabilitation. The inspection HOQ requires input from customer as well as routine maintenance results (Objective 2). The routine maintenance results will be used for condition assessment (Objective 1), from which condition indices are obtained. If primary and secondary condition indices are greater than 1 and a decision is required, the replacement and rehabilitation HOQs can be put into action (Objective 3). This requires input from the customer along with means of satisfying the customer under social, economic, safety issues, maintenance efficiency and environmental related areas (also termed as "focus areas" in this thesis). In the absence of dedicated survey data for the replacement and rehabilitation QFDs, existing customer surveys on the infrastructure condition can be adopted within a Hidden Markov Model (HMM) for forecasting customer requirements (Objective 4). For decision-making between rehabilitation and replacement scenarios, maximum scores obtained from the QFD HOQs can be used for choosing between the two scenarios.   44                              Figure 2-4 Proposed Approach OBJECTIVE 2 (CHAPTER 4) OBJECTIVE 4 (CHAPTER 5) OBJECTIVE 1 (CHAPTER 3) OBJECTIVE 3  (CHAPTER 4) REHABILITATION User Input REPLACEMENT User Input Social Economic Safety Issues Maintenance Efficiency Environmental Inspection Manual Hierarchical ER Framework Interval -Based Condition Ratings Inspection Item List Classify Elements INSPECTION PRIORITIZATION User Input Primary & Secondary Indices > 1.0 Tertiary & Life-Safety Critical Indices > 1.0 Decision Required Score for each Issues Maximum Score for Rehabilitation Maximum Score for Replacement Rehabilitate Replace Condition Indices All Indices < 1.0 Any Index > 1.0  CUSTOMER REQUIREMENTS (CRs) FOR QFD INPUT USER SURVEY AT TIME `(t-1)` known PARAMETERS @ time (t-1)  OBSERVED parameters  @ time (t) HIDDEN MARKOV MODEL (HMM) Social Forecast Economic Forecast Safety Issues Forecast Maintenance Efficiency Forecast Environmental Forecast   45 Chapter  3: Hierarchical Evidential Reasoning (HER) Framework for Condition Assessment of Bridges A version of this chapter has been published in the Journal of Structure and Infrastructure Engineering. Bolar, A., Tesfamariam, S., & Sadiq, R. (2012a). "Condition assessment for bridges: A hierarchical evidential reasoning (HER) framework." Structure and Infrastructure Engineering, 9(7) 648-666. doi: 10.1080/15732479.2011.602979  3.1 Background General information about bridge management systems (BMS), both North American and internationally is provided in Chapter 2. In this section, an overview of practical condition assessment for bridges is presented followed by implementation of the proposed Objective 1. Most bridge management agencies have developed effective inspection practices through quality assurance/control (QA/QC) programs. The National Bridge Inspection Standards (NBIS) was established in 1971 to provide guidelines and uniform criteria for various highway agencies. The standards are based on the AASHTO manual for maintenance inspection of bridges. The objective of NBIS is to specify inspection requirements described in general as follows (White et al. 1992): • Inspection Personnel: A team of two to six members; directed by a licensed engineer • Inspection Frequency: Detailed inspection every two years. Interim inspections at any other frequency depending on problem areas • Records:  o An "appraisal rating" which is a numerical score for each of the major components of the present component relative to current desirable characteristics   46 o A "sufficiency rating" to indicate bridge sufficiency to remain in service; 100% represents an entirely sufficient bridge and 0% represents a deficient bridge • Inspection Types:  o Routine Inspection: For identifying physical and functional condition of the bridge for identifying developing problems or changes from a previous condition o Damage Inspection: Unscheduled inspection to assess structural damage from exogenous events • Rating: Permissible operating load determined for each structure. Normally equal to the maximum weight of a standard (HS) truck • Techniques: Survey requirements such as datum, stream or channel profile. This step is normally carried out first for the crew to gain familiarity with the bridge These initiatives have led to the development of various technologies and techniques during the last few years to inspect/monitor bridge systems. The NBIS was introduced as a result of the Federal Highway Act of 1968 and consists of a component recording system which is still in practice. The 1991 Intermodal Surface Transportation Efficiency Act (ISTEA) mandated each state to develop a Bridge Management System (BMS). This led to the use of Pontis® a federally advocated, computer-based BMS model and allowed more details of individual bridge elements (AASHTO 1997). This "element level" rating system is part of the current Bridge Management System (BMS) and is further explained in the current bridge maintenance section of this thesis. A summary of expert systems for damage assessment of bridges was provided by Liu (1998). Recent work on application of soft computing techniques for bridges is summarized in Table 3-1 Fault trees have been used to identify failure of bridge structures (Johnson 1999; Hadipriono 2001; Choi et al. 2005; LeBeau et al. 2007). Most of these studies have used probability   47 assessment or Bayesian approach (Choi et al. 2005). Bayesian belief network approach has been applied by Attoh-Okine and Bowers (2005), whereas the evidential reasoning approach has been explored by Wang and Elhag (2006).  An overall decision-making process generally requires more than one piece of information (generally termed as element or data). In probabilistic terms, sets consisting of such single elements are referred to as singletons.  However, in most engineering situations, more than one type of data is required to make informed decisions. Data fusion is a process of combining diverse data sets in a reproducible and objective way. For example, condition assessment of a bridge substructure may involve two measurements - one for the settlement and another for scour. Data fusion principles would enable the combination of these two sets of information which are different in character, measurement scale and value. If different data sets are available that provide information on various aspects of the problem, they are referred as complementary. Therefore, the efforts would be aimed towards obtaining more information for making reliable decisions. On the other hand, information provided by the various data sets can be sometimes redundant, e.g. dealing with the same aspect of the problem without providing any additional insight. This may seem inessential; however, the additional data sets can improve reliability of the information, if the interpretation of one data set is confirmed by the other. Complementary and redundancy of data sets are the basis of a data fusion application (Kaftandjian and Francois 2002). The Dempster-Shafer theory (DST) can be interpreted as a generalization of the Bayesian theory where probabilities are assigned to subsets and not only to mutually exclusive singletons. The   48 Table 3-1 Application of Soft Computing to Bridges Author Year Evaluation Type Assessment Type Knowledge Representation Uncertainty Representation Chiang et al. 2000 Fuzzy Petri Net Based Expert System Damage Hierarchical Fuzzy Petri Nets Fuzzy Truth Value Ming-Te Liang et al. 2001 Multiple Layer Fuzzy Evaluation Damage Multiple Layer Fuzzy None Zhao and Chen  2001 Fuzzy Inference System Deterioration Modified Mountain Clustering Method (MMM) None Lin et al. 2002 Neural Network Based Methodology Seismic Damage Neural Networks None Estes and  Frangopol 2003 Updating Existing Visual Inspection Results Reliability Bayesian Updating None Kei Kawamura and Miyamoto 2003 Neuro-fuzzy hybrid system Deterioration Neural Network None Sasmal et al. 2006 Fuzzy Logic Based Condition Rating Condition Assessment Multi-Attributive Decision Making (MADM) model Fuzzy Logic Wang and Elhag 2006 Fuzzy TOPSIS method Risk Assessment Alpha Sets - Non Linear Programming (NLP) None Sasmal and Ramanjaneyulu 2008 fuzzy based analytic hierarchy approach Condition Assessment Analytic Hierarchy Process (AHP) using MADM model Optimistic fuzzy membership function Wang and Elhag 2008 Evidential Reasoning Approach Condition Assessment Recursive Evidential Reasoning Algorithm Normalization   49 applications of DST vary from buried pipes (Bai et al. 2008), fault diagnosis of machines (Fan and Zuo 2006), structural systems (Bae et al. 2004), environmental decision-making (Attoh-Okine and Gibbons 2001; Chang and Wright 1996) to seismic risk management (Tesfamariam et al. 2010). Many more engineering applications of DST can be seen in detailed bibliography provided by Sentz and Ferson (2002).  In this study, a hierarchical evidential reasoning (HER) framework is proposed for the condition assessment of bridges. The HER framework involves classifying bridge data into Primary, Secondary, Tertiary and Life Safety-Critical elements. The HER framework has been adopted from Bai et al. (2008), which was originally applied for condition assessment of buried water mains. The data is systematically combined using evidence theory to obtain respective condition indices and finally compute the overall bridge condition index (BCI).  3.2 Bridge Hierarchical Evidential Reasoning (HER) Framework 3.2.1 Bridge Management Systems (BMS) The innovations in computing along with the introduction of asset management concepts in bridge maintenance had prompted bridge stakeholders in the US to adopt a Bridge Management System (BMS). BMSs are decision support tools developed to assist in determining how and when to make bridge investments that will improve safety and preserve existing infrastructure (Asset Management Primer 1999). In doing so, from an engineering standpoint, the current bridge condition state is mostly relied upon by effective inspection practices. The national co-operative highway research program report 375 (NCHRP 2007) provides exhaustive information on inspection practices in the US and selected foreign countries.  As per the Bureau of Transportation Statistics (BTS 2009), there are 600,000 bridges in US. Nearly 40% of those bridges are considered deficient and are eligible for funding under the   50 Highway Bridge Replacement and Rehabilitation Program (Frangopol 2002). Pontis® is the most commonly adopted BMS with relevant modifications to suit each state's bridge inventory type. Pontis® was adopted by AASHTO as an AASHTOware product in 1994 and by individual states at various times between the years 1995-2005.  Pontis® uses a National Bridge Inventory (NBI) rating evaluated for a larger group of bridge elements, such as deck, superstructure, substructure, and culverts. Pontis® also requires a more refined condition rating by inspecting the bridge at an element level what are known as AASHTO Commonly Recognized (CoRe) elements (AASHTO 1997). Table 3-4 & Table 3-5 show the bridges components (elements) referred from the Colorado Department of Transportation (CDOT) Bridge Inspection Guide (CDOT 1998). Each element inspection is quantified by three to five condition states represented by, CS-1 to CS-5, corresponding to Condition State 1, to 5, respectively. Condition state 1 represents good (low damage) state and Condition 5 represents bad (deteriorated) state.  Canadian bridge agencies operate at three different levels (a) National by the Transport Canada (b) Provincial/ Territorial by the Ministries of Transport, and agencies at the (c) Municipal or local level (NCHRP 2007). Therefore, bridges in Canada are maintained at three management levels depending on the authoritative agency of the bridge.  3.2.2 HER Based Health Indices Performance based indices have been used to as an indicator of bridge condition. Frangopol and Neves (2008) have used a condition index and safety index that respectively represent the effects of deterioration and safety margin of the structure. Scherschligt and Kulkarni (2006) proposed Pontis® based health indices for the state of Kansas as an alternative to a single Bridge Health Index based on NBI condition ratings. Prior to this, Shepard and Johnson (2001) proposed a single number health index for bridge condition evaluation based on element level inspection for   51 the state of California. The rationale was to avoid duplication of inspection/data between Pontis® and NBI condition rating and also to make more efficient use of the element level inspection recorded in Pontis®. In this study, a systematic way of grouping Pontis® condition states into a Hierarchical Evidential (HER) Framework is proposed.  Similar classification of elements has been used for example in repair classification of aircraft structures (Baker et al. 2004). Following are some key terminologies defined: Primary Elements are those whose failure could cause bridge collapse or catastrophic consequences. Deck, superstructure, and substructure are grouped as primary. Fracture critical elements are included as primary elements. However, depending on the type of bridge material (i.e. steel), fracture critical element could be grouped separately. Secondary Elements are those whose failure will not cause overall bridge collapse. Examples are berms, culverts, wing walls, etc. Tertiary Elements are those whose failure will cause negligible effect on bridge collapse. Examples are coatings, linings, etc.  Life Safety-Critical Elements are those whose failure will have no effect on bridge collapse, but are deemed critical from a safety point of view. An example would be a railing which if broken will have no effect on bridge collapse, but can nevertheless be dangerous to the bridge users. Exogenous Parameters are defined as those "rare" parameters that can cause catastrophic failure. Examples could include overload of the bridge, natural events such as wind gusts, earthquake, floods, etc.    52 Endogenous Parameters are defined as those parameters that lead to deterioration of bridge under normal operation. Examples include normal wear and tear, exposure to environment, age of the bridge, etc.  A variety of condition rating schemes (scales) has been adopted by each BMS either in practice or research (Wang 2008). This approach deviates from a preferred engineering approach of standardization. If a common condition rating scheme was adopted by every BMS in the world, this could lead to numerous advantages such as comparison and knowledge sharing of bridges with similar loading, relate bridges with similar regimes of natural events and environment, compare inspection schemes, etc. With this objective, the focus of condition rating scheme in the current study was to demonstrate that existing bridge components can be grouped systematically into Primary, Secondary, Tertiary and Life Safety-Critical Elements and corresponding set of indices can be generated. Table 3-2 shows condition rating granularities of various BMS and references as reported by Wang (2008) along with condition scales in the current HER framework. The proposed classification of existing elements and smartflags are also shown in Table 3-4 and Table 3-5 respectively. This list is not conclusive as historical maintenance data on a particular bridge could provide insight into a more appropriate categorizing of elements. For example, Dornsife (2000) reported that expansion joints absorb secondary stresses due to misalignment, but in extreme cases expansion joints could cause catastrophic failure. Hence a decision-maker could either group these as anything other than secondary elements (Life Safety-Critical for example) depending on the inspected condition. Alternatively, in the current study, importance factors are used for each element that could be appropriately assigned in these special situations.      53  Table 3-2 Condition evaluation granularity in BMS/research [Reported by Wang (2008)] Condition Scale Bad                                                                   Good BMS/references Condition Assessment Representation NBI condition ratings 0 1 2 3 4 5 6 7 8 9 New York BMS 1 2 3 4 5 6 7 Denmark MBS 5 4 3 2 1 0 Virginia BMS 3 4 5 6 7 8 9 Swiss BMS 5 4 3 2 1 Liu et al. (1997a; 1997b); Liang et al. (2001) I II III IV V Frangopol et al. (2001) 1 2 3 4 5 HER CS5 CS4 CS3 CS2 CS1  3.3 Basic HER framework A generic procedure to combine attributes or parameters was developed in the previous subsection. In a hierarchical framework, the attribute at a higher-level is evaluated based on the assessment of its associated lower-level parameters as illustrated in Figure 3-1. In this section, a general description of the attributes and parameters is provided. In the proposed HER model, the condition rating of the kth attribute, Ek, is evaluated based on a number of parameters, which can be directly observed or estimated. The evaluation of an attribute Ek with contributory parameters ike (i = 1, 2, …, Lk) is given by, Ek =1ke ⊕ 2ke ⊕ … ⊕ kLke          (3-1) where Lk denotes the number of parameters that contribute to the kth attribute. Each parameter can be treated as a body of evidence, which can be aggregated using DS rule of combination, Table 3-3 provides a general scheme for combining two bodies of evidence using the DS rule of   54 combination. Detailed literature review is available in Chapter 2 and worked examples in Appendix A.  The evaluation of each parameter ike  is obtained by mapping  Table 3-3 The D-S Rule of Combination for Two Bodies of Evidence  Joint body of evidence( )( ))2(Ikem  Second body of evidence (parameter), ( )21em  {H1} … {Hn} … {HN} {H} First body of evidence (parameter), ( )11em {H1} {H1}/ ( 11,Hkm12,Hkm ) … {Φ}/  ( 11,HkmnHkm 2, ) … {Φ}/    ( 11,HkmNHkm 2, ) {H1}/ ( 11,HkmHkm 2, ) … … … … … … … {Hn} {Φ}/  ( 11,HkmnHkm 2, ) … {Hn}/ ( nHkm 1,nHkm 2, ) … {Φ}/    ( nHkm 1,NHkm 2, ) {Hn}/ ( nHkm 1,Hkm 2, ) … … … … … … … {HN} {Φ}/ ( NHkm 1,12,Hkm ) … {Φ}/ ( NHkm 1,nHkm 2, ) … {HN}/  ( NHkm 1,NHkm 2, ) {HN}/ ( NHkm 1,Hkm 2, ) {H} {H1}/ (Hkm 1,12,Hkm ) … {Hn}/ (Hkm 1,nHkm 2, ) … {HN}/  (Hkm 1,NHkm 2, ) {H}/ (Hkm 1,Hkm 2, )  inspection/ observation results on a pre-defined scale of condition states (universe of discourse) for the overall structure. The BPA for each parameter can be derived based on a degree of confidence estimated/assigned to the condition states, as well as the associated importance and reliability of the data (or a credibility of an experts' judgment).  Although DST can handle interval based data, condition states or evaluation grades are assumed mutually exclusive and exhaustive. Therefore, it is necessary to define condition states as disjoint singletons, which encompass all possible condition states that can be expressed by the particular   55 parameter. Assume that the frame of discernment, H, to describe the condition states described by a parameter as: H = {H1, H2, …, Hn, …, HN};   n = 1, …, N       (3-2) where N is the number of possible condition states, Hn represents the nth condition state, and H1 and HN are the best and the worst possible condition states, respectively. An expert may not always be 100% sure that the condition state is exactly confined to only one condition states. In most instances, condition rating will be confined to two or no more than three contiguous condition states with a total degree of confidence equal or smaller than 100%. The hierarchical grouping of existing Pontis® elements is summarized in Table 3-4 & Table 3-5. Once the elements are grouped into the hierarchical framework, mapping of data from other evaluation techniques into current HER framework can be done using Table 3-6.     56  ⊕ …  … 11e  11Le  ⊕ Bridge Condition Index E2 (Secondary CI) m( 12e )= S(12e )×12λ  m( 22Le )=S( 22Le )× 22lλ   22Le   … 12e  E3 (Tertiary CI) ⊕ m( 13e )= S(13e )×13λ  m( 33Le )=S( 33Le )× 33lλ   33Le   13e  E4 (Life Safety Crit. CI) ⊕ m( 14e )= S(14e )×14λ  m( 44Le )=S( 44Le )× 44lλ   44Le   14e  ⊕ … m( 11e )= S(11e )×11λ  m( 11Le )= S( 11Le )× 11Lλ  Attribute Level Model Input for assigning Basic Probability Assignments (BPAs) Parameter Level E1 (Primary CI) Figure 3-1 Generic Bridge Hierarchical Evidential Reasoning (HER) Framework   57 For example, referring to Table 3-4 consider the culverts portion of the HER framework in terms of attributes and parameters. The overall condition rating in this case comprises of Steel Culvert (240-4), Concrete Culvert (241-4), Timber Culvert (242-4), and Other Culvert (243-4).  For a given bridge, just one of the items will apply. The approach proposed in the current study is to classify all elements into Primary/Secondary/Tertiary/Life Safety-Critical and generate corresponding indices. Furthermore, the Primary/Secondary/Tertiary/Life Safety-Critical indices generated for each bridge in a given inventory can be combined to generate overall indices for the bridge inventory. Therefore, as an example, for secondary condition index the secondary elements of the bridge are assumed to consist of culverts alone (as an example for demonstrating the combination process).  Culvert in Pontis® is represented by four condition states, which can be obtained from direct inspection or observation. The condition rating of, say, culvert at the attribute level E1 is based on four contributory parameters as follows: 1. Steel Culvert ( 11e ): CS-3 and CS-2 with a 60% and 20% degree of confidence, respectively; 2. Concrete Culvert ( 21e ): CS-3 and CS-2 with a 70% and 30% degree of confidence, respectively;  3. Timber Culvert ( 31e ): CS-3 and CS-2 with a 75% and 10% degree of confidence, respectively; 4. Other Culvert ( 41e ): CS-1 and CS-2 with a 50% and 15% degree of confidence, respectively.    58 Table 3-4 Proposed classification of the Colorado Department of Transportation (CDOT) Pontis® Elements  Here, the frame of discernment, H, for each of these parameters consists of five condition states, namely, CS-1, CS-2, CS-3, CS-4, CS-5 where CS-1 is the "No Damage" condition state and CS-5 is "Severe Damage" condition state.   H = {CS-1, CS-2, CS-3, CS-4, CS-5}       (3-3)   Classification Designation Material/Description Primary Deck Concrete, Steel, Composite, Timber, Railroad Deck Slab Concrete Slab Super Structure Concrete, Steel, Timber, Other (Masonry) Substructure Concrete, Steel, Timber, Other (Masonry) Secondary WingWalls Slope Protection, Berms, etc. Approach Slab Concrete Bearings Elastomeric, Moveable, Fixed Joints Expansion, Seal, Elastomeric, Construction Culverts Steel, Concrete, Timber, Other Tertiary Sidewalks Metal , Concrete, Timber Coatings Substructure and Superstructure Tunnel Lining Concrete Lined , Shotcrete Lined, Unlined Channel/RWA/General Channel, Bank, Debris, Waterway Adequacy, Approach Roadway Alignment, General Remarks Life Safety- Critical Railing Concrete, Timber, Metal, Misc Flag/Pole Sign Attachment to Bridge   59 Table 3-5 Proposed classification of the Colorado Department of Transportation (CDOT) Pontis® SmartFlags Classification Description Primary Exogenous 355*-3- Steel Diaphragms 356 -3- Steel - Fatigue 399*-5- Alkali-Silica Reactivity (ASR) Endogenous  358 -4- Deck Surface Cracking 360 -3- Settlement 361 -3- Scour 362 -3- Traffic Impact (Superstructure) 370*-3- Traffic Impact (Substructure) 371*-3- Traffic Impact (Deck) Secondary Exogenous  359 -5- Soffit of Concrete Decks and Slabs 372*-3- False Bent/Temporary Support 373*-4- Pack Rust (Substructure) Endogenous 357 -4- Pack Rust (Superstructure) In the above assessment, the degrees of confidence (βn,i) 60%, 20%, 70%, 30%, 75%, 10%, 50% and 15% are referred to BPAs obtained from a Bridge Inspector’s experience and/or related to inspection precision. The sum of the degrees of evidence for each parameter is incomplete if less than 1. For example, the missing BPA of 0.2 in Steel Culvert represents ignorance or epistemic uncertainty. The second body of evidence (Concrete Culvert) is complete because total assigned BPA is 0.7 + 0.3 = 1. The condition rating (S) for a given parameter ike can be written as,   60 S(ike ) = {(Hn / βn,i), n = 1, …, N};   i = 1, 2, …, Lk    (3-4) where βn,i ≥ 0 and ∑=Nnin1,β ≤ 1. Thus, the parameter, ike , can be assessed to grade Hn with a degree of confidence βn,i. An assessment is complete if ∑=Nnin1,β = 1, and is incomplete if ∑=Nnin1,β < 1. A special case occurs when ∑=Nnin1,β = 0, which means that there is no information on parameter ike , i.e., a ‘vacuous’ evidence. Following Eqn. (20), the parameters that contribute to the attribute culvert (E1) can be described as follows: S (Steel Culvert) = {CS-3/0.6, CS-2/0.2} S (Concrete Culvert) = {CS-3/0.7, CS-2/0.3} S (Timber Culvert) = {CS-3/0.75, CS-2/0.10} S {Other Culvert} = {CS-1/0.50, CS-2/0.15} In practice, not all the parameters have the same importance towards the assessment of an attribute. In addition, the data collected from different sensors may be erroneous (less reliable) or expert judgment may have different levels of credibility. Such credibility is assigned by using a reliability factor which ascertains the reliability of the data. Similarly, each condition index could be assigned different importance which is represented by an importance factor. The importance and reliability factors are lumped together into a parameter, ikλ , which is normalized relative to the weight of evidence for a parameter, ike , towards the evaluation of an attribute, Ek. Therefore, the weight matrix for an attribute, Ek, can be written as,   61  10where},,...,,{ 1 ≤≤= ikLkikkkk λλλλλ        (3-5) The BPA m( ike ) for a parameter ike can be determined discounting S by βn,i. m( ike ) = S(ike )×ikλ = {(Hn/ nHikm , ); n = 1,2, …, N}      (3-6) where nHikm , =ikλ βn,i  and Hikm , = ∑=−Nninik1,1 βλ   If only one contributory parameter, say 1ke , is associated with Ek, then the condition rating for an attribute, Ek, will be exactly confirmed by m(1ke ). 3.4 Application of HER Framework  In order to demonstrate use of HER framework in the manner described in this study, data for Huey Tong Bridge in Taipei as reported in Liang (2001) was adopted. The first step in the process of application was mapping the data from the "evaluation content" of the adopted data to a BPA-based condition rating of each possibility.  The BPA possibilities used in the current study are CS-1, CS-2, CS-3, CS-4, CS-5., where CS-1 to CS-5 successively represents "No Damage" condition state to "Severe Damage" condition state.  The advantage of using HER framework is also the use of interval BPAs. For example, one could rate a particular parameter as having probability of 95% CS-4 and 5% CS-3. A rational review of the condition state of each evaluation parameter in Liang (2001) was done in order to determine where best the probability may lie. Furthermore, Liang (2001) had four condition states compared to five condition states in the current study. Therefore, with the finer granularity, severe damage for example, was qualified as {95% CS-5 and 5% CS-4}. A case of light damage was qualified as {15% CS-2; 75% CS-3; 10% CS-4}. Table 3-6 provides the mapping information used to arrive at the condition ratings.   62 The next step in the process of using the adopted data was to build a hierarchical tree that could be used for combination. Figure 3-2 shows the hierarchical tree generated for Huey-Tong Bridge. Primary elements of the structure were grouped together under a "Primary Condition Index" and secondary elements of the structure under a "Secondary Condition Index." The rationale for classifying the elements into primary and secondary is shown in Table 3-6. Finally the Primary and Secondary Condition Indices were grouped together to arrive at a overall Bridge Condition Index (BCI). For primary elements, a level has been added for "Demand" and "Capacity". The reason for adding them to the HER was to illustrate that a demand analysis under extreme events can be performed if required.  The DS and Yager rule of combinations along with the use of appropriate credibility factors are demonstrated by choosing the secondary condition index hierarchical portion as an example. The secondary condition index consists of   (a) S( 11e ) → Surface Roughness of Wear Layer {95% CS-1; 5% CS-2}   (b) S( 21e ) → Wear Layer Thickness {95% CS-1; 5% CS-2}, and   (c) S( 11e ) →  Expansion Joints {5% CS-4; 95% CS-5}.  Assuming the surface roughness and thickness of wear layer would be easily measurable, a reduced reliability factor of 0.6 was assigned. The expansion joints in the adopted data was reported "Bad (1.0)." Any severe damage reported could be (or should be) interpreted as relatively more credible as "No Damage" since any damage reported must have been based on actual visual deterioration. Hence a reliability factor of 0.95 was used. On the contrary, there is a     63   Figure 3-2 Huey-Tong Bridge Data from Liang (2001) in Proposed Hierarchical Evidential Reasoning (HER) Framework good possibility that a structure inspected as "defect-free" could have underlying deterioration that might be hard to identify depending on the type of inspection adopted; deterioration might have been missed and therefore erroneously reported as "No Damage". Therefore, the reliability factor could be reduced for cases of "No Damage". The assigning of importance factor was based on the relative importance of the elements. Expansion joints were judged as relatively more important than wear layer thickness/roughness and therefore importance factors were chosen as 0.8 and 1.0, respectively. Table 3-7 provides the criteria for choosing relevant credibility factor. The criterion is termed "hypothetical" as actual inspection documentation was not available for the current study. Evidential ReasoningBRIDGE CONDITION INDEXLIMITING WEIGHT UNUSUAL SAFETY CRITICAL LOAD  EXOGENEOUS PARAMETERSPRIMARY CONDITION INDEXSECONDARYCONDITION INDEXSURFACE ROUGHNESSOF WEAR LAYERWEAR LAYER THICKNESSEXPANSION JOINT DESIGN LOADHEAVY VEHICLE TRAFFICSTRUCTURAL TYPEENDOGENEOUS PARAMETERSDECK SUPER-STRUCTURE SUPPORTED STATUSSUM OF CAPBEAM CAPBEAM GIRDERSUB-STRUCTURE CAPBEAM, PIER,DECK AND FOUNDATIONCAPACITYDEMAND  64 Table 3-6 Mapping of data from Liang (2001) to proposed HER framework Note  a: The values in this column represent number of possibilities for each evaluated parameter.    b: Liang (2001) rating ranges from 1.0 (Severe Damage) to 0.0 (Non Damage); Rating in the current study ranges from CS-1(No Damage) to CS-5 (Severe); CS stands for "Condition State"   LIANG (2001) MAPPING CS-1 CS-2 CS-3 CS-4 CS-5   Note a EVALUATION b Note a Mapping Criteria Condition States EVALUATION b   Concrete Deck 4 Non Damage (0) Light Damage (0.25) Moderate Damage (0.5) Severe Damage (1.0) 5 Severe Damage. CS-4 to CS-5 CS (4,5) 0 0 0 0.05 0.95 PRIMARY Girder 4 Non Damage (0) Light Damage (0.25) Moderate Damage (0.5) Severe Damage (1.0) 5 Severe Damage. CS-4 to CS-5 CS (4,5) 0 0 0 0.05 0.95 Sum of Capbeam 1    0 5 No Damage. CS-1 to CS-2  CS(1,2) 0.95 0.05 0 0 0 Capbeam Function 3  Good (0) Acceptable (0.5) Bad (1.0) 5 No Damage. CS-1 to CS-2  CS(1,2) 0.95 0.05 0 0 0 Supported Status 3  Good (0) Acceptable (0.5) Bad (1.0) 5 No Damage. CS-1 to CS-2  CS(1,2) 0.95 0.05 0 0 0 Capbeam, Pier, Deck, and Foundation 4 Non Damage (0) Light Damage (0.25) Moderate Damage (0.5) Severe Damage (1.0) 5 "Light Damage" CS-2/CS-3/CS-3 CS (2,3,4) 0 0.15 0.75 0.1 0 Design Loading 3  HS-20 + 25% above (0) HS-20+0-25% (0.5) HS-20 (1.0) 5 "1 for HS-20; Lesser overload capacity " Hence CS-4 to CS-5 CS(4,5) 0 0 0 0.05 0.95 Traffic of Heavy Vehicle 3  0-1000 (0) 1000-2000 (0.5) 2000 Above (1.0) 5 "0" Hence CS-1 to CS-2 CS(1,2) 0.95 0.05 0 0 0 Structural Type 2   Other Supports (0.5) Simple Support (1.0) 5 "0.5 Non-Simple support i.e redundant CS-1/CS-2/CS-3 CS(1,2,3) 0.1 0.2 0.7 0 0 Limiting Weight and Limiting Speed 3  Both (0) One of them (0.5) None (1.0) 5 "No Limiting Weight/Speed" Overload Possible; CS-4 to CS-5 CS(4,5) 0 0 0 0.05 0.95 Unusual Phenomenon of Loading Safety 1    0.5 5 "0.5"  mapped as CS-3 to CS-4 CS(3,4) 0 0 0.75 0.25 0 Surface Roughness of wear Layer 3  Smooth (0) Light Rough (0.5) Severe Rough (1.0) 5 No Damage. CS-1 to CS-2  CS(1,2) 0.95 0.05 0 0 0 SECONDARY Wear Layer Thickness 1    0 5 No Damage. CS-1 to CS-2  CS(1,2) 0.95 0.05 0 0 0 Expansion Joints 3  Good (0) Acceptable (0.5) Bad (1.0) 5 Severe Damage. CS-4 to CS-5 CS(4,5) 0 0 0 0.05 0.95   65 Table 3-7  Credibility factors and criteria for classifying bridge elements used in Liang (2001) Item Classification Criteria Reliability/ credibility Factor Hypothetical Criterion for Deciding RF closer to 1 Concrete Deck Primary Failure can lead to collapse 0.95 Deck was probably easily inspectable; Damage Reported Girder Primary Failure can lead to collapse 0.95 Girder was probably easily inspectable; Damage Reported Sum of Capbeam Primary Failure can lead to collapse 0.60 Not easily inspectable; No Damage Reported Capbeam Function Primary Failure can lead to collapse 0.60 Not easily inspectable; No Damage Reported Supported Status Primary Failure can lead to collapse 0.60 Not clear if "other supports" mean redundancy Capbeam, Pier, Deck and Foundation Primary Failure can lead to collapse 0.60 Not easily inspectable; No Damage Reported Design Loading Primary Exceeding Limits can lead to collapse 0.90 Design Loads might be readily available Traffic of Heavy Vehicle Primary Exceeding Limits can lead to collapse 0.60 Low Traffic Weight; Room for Exceedance Structural Type Primary Existing support type can lead to collapse or redistribution 0.85 Not clear if "other supports" mean redundancy Limiting Weight and Limiting Speed Primary Exceeding Limits can lead to collapse 0.90 No Limiting Weight; Overload Possible Unusual Phenomenon of Loading Safety Primary Catastrophic Failure Possible 0.75  Surface Roughness of Wear Layer Secondary Failure will transfer loads to primary elements 0.60 Not easily measureable; Wear Layer Thickness Secondary Failure will transfer loads to primary elements 0.60 Not easily measureable; Expansion Joints Secondary Failure will transfer loads to primary elements 0.95 Probably well inspectable. Damage Reported    66 3.4.1 Illustrative Evaluation of Secondary Condition Index: D-S Rule of Combination The condition rating S( ike ) for each parameter is provided as a degree of confidence (Hn/βn,i)  S( 11e )  =  {CS-1/0.95, CS-2/0.05, CS-3/0, CS-4/0, CS-5/0}  S( 21e ) =  {CS-1/0.95, CS-2/0.05, CS-3/0, CS-4/0, CS-5/0}  S( 31e ) =  {CS-1/0, CS-2/0, CS-3/0, CS-4/0.05, CS-5/0.95}  The weights (importance & credibility) for each contributory parameter to the attribute Es: 1λ = {11λ ,21λ31λ }T = {0.48, 0.48, 0.95}T   The credibility factor is multiplied with the condition ratings; the difference between 1.0 and sum of condition ratings implies the ignorance or epistemic uncertainty (H). 11λ S(11e )  =  {CS-1/0.76, CS-2/0.04, CS-3/0, CS-4/0, CS-5/0 , H/0.2} 21λ S(21e ) =  {CS-1/0.76, CS-2/0.04, CS-3/0, CS-4/0 CS-5/0, H/0.2} 31λ S(31e ) =  {CS-1/0, CS-2/0, CS-3/0, CS-4/0.05 CS-5/0.95, H/0.0} The aggregation of parameters for the attribute, Secondary Condition Index (SCI), is given by: Secondary Condition Index (SCI) = 11λ S(12e ) ⊕ 21λ S(22e ) ⊕ 31λ S(32e )   (3-7) Therefore, the BPA for each parameter can be written as, m1,1 = {HH mm n 1,11,1 , } = {0.46, 0.02, 0, 0, 0, 0.52} m1,2 = {HH mm n 2,12,1 , } = {0.46, 0.02, 0, 0, 0, 0.52}      (3-8) m1,3 = {HH mm n 3,13,1 , } = {0, 0, 0, 0.05, 0.90, 0.05} Using the recursive DS rule of combination (Eqn. 16), the combined probability assignments can be determined as follows. Initially, we take 1,1)1(1 mmI =  according to the idempotency property of   67 DS rule of combination. Now we aggregate the first two parameters, namely, Surface Roughness of Wear Layer and Wear Layer Thickness using the DS rule of combination: 1414,12,1)1()2( )1( 11−= ≠=∑ ∑−=s slllsII mmK    = [1 - (0 + … + 0 + 51412131 2,11,12,11,12,11,12,11,1HHHHHHHH mmmmmmmm +++ + 0)]-1   (3-9) = [1 - (0.46 × 0.02 + 0.02 × 0.46)] –1 = 1.02  Therefore, the combined BPAs are  )( 1111111 2,11,12,11,12,11,1)2()2(HHHHHHIHI mmmmmmKm ++= = 1.02×(0.46×0.46 + 0.46×0.52 + 0.52×0.46) = 0.70 )( 2222121 2,11,12,11,12,11,1)2()2(HHHHHHIHI mmmmmmKm ++= = 1.02×(0.02×0.02 + 0.02×0.05 + 0.02×0.05) = 0.03 )( 3333131 2,11,12,11,12,11,1)2()2(HHHHHHIHI mmmmmmKm ++= = 0 )( 4444141 2,11,12,11,12,11,1)2()2(HHHHHHIHI mmmmmmKm ++= = 0 )( 5555131 2,11,12,11,12,11,1)2()2(HHHHHHIHI mmmmmmKm ++= = 0 HHIHI mmKm 2,11,1)2()2( 11 =  = 1.46 × (0.1 × 0.55) = 0.28. Combining the above results with the third parameter, namely, expansion joints, as follows, 1414,13,1)2()3( )1( 11−= ≠=∑ ∑−=s slllsII mmK = [1 - 0.70 × 0.05 + 0.70 × 0.90 + 0.03 × 0.05 + 0.03 × 0.90] –1 = 3.20 The combined BPAs for the three parameters are )( 1111111111 3,1)2(3,1)2(3,1)2()3()3(HHIHHIHHIIHI mmmmmmKm ++= = 0.11 )( 2121221121 3,1)2(3,1)2(3,1)2()3()3(HHIHHIHHIIHI mmmmmmKm ++= = 0 )( 3131331131 3,1)2(3,1)2(3,1)2()3()3(HHIHHIHHIIHI mmmmmmKm ++= = 0   68 )( 4141441141 3,1)2(3,1)2(3,1)2()3()3(HHIHHIHHIIHI mmmmmmKm ++= = 0.4 )( 5151551151 3,1)2(3,1)2(3,1)2()3()3(HHIHHIHHIIHI mmmmmmKm ++= = 0.80  HHIIHI mmKm 3,1)2()3()3( 111 = = 0.04.  Therefore, the final rating for secondary condition index (E2) is {CS-1 / 0.11, CS-2 / 0, CS-3 / 0, CS-4 / 0.4, CS-5 / 0.80}. Since the conflict between the data was normalized by K, the combined data does not possess much contribution from conflict which might actually be valuable in making a good decision. The degree of confidence for the bridge secondary elements as Condition State 5 is highest at 80%. However, this condition rating assessment is based on information from the third attribute Expansion Joints since the reliability factor for this parameter was 0.95 compared to 0.60 for the remaining parameters. If the reliability factor of all three parameters were kept the same at 0.95, the degree of confidence is evaluated as CS-1, 94.2% corresponding to the first two parameters.  3.4.2 Illustrative Evaluation of Secondary Condition Index: Yager Rule of Combination Yager rule differs from DS combination rule in handling conflict that is represented by k in DS rule. The conflict attributed to k is shifted to ignorance instead of normalization process. )(414,12,1)1()2( 11 ∑ ∑= ≠==s slllsII mmK         (3-10)  = [(0 + … + 0 + 51412131 2,11,12,11,12,11,12,11,1HHHHHHHH mmmmmmmm +++ + 0)]-1 = [(0.46 × 0.02 + 0.02 × 0.46)] = 0.02  The combined BPAs for the first two parameters are: )( 111111 2,11,12,11,12,11,1)2(HHHHHHHI mmmmmmm ++= = (0.46×0.46 + 0.46×0.52 + 0.52×0.46) = 0.68 )( 222221 2,11,12,11,12,11,1)2(HHHHHHHI mmmmmmm ++= = 0.02×0.02 + 0.02×0.05 + 0.02×0.05) = 0.03   69 )( 333331 2,11,12,11,12,11,1)2(HHHHHHHI mmmmmmm ++= = 0 )( 444441 2,11,12,11,12,11,1)2(HHHHHHHI mmmmmmm ++= = 0 )( 555551 2,11,12,11,12,11,1)2(HHHHHHHI mmmmmmm ++= = 0 HHIHI mmKm 2,11,1)2()2( 11 +=  = 0.02 + (0.52 × 0.52) = 0.29. Similarly, combining with the third parameter i.e. expansion joints, using Yager rule, the final rating for secondary condition index (E2) is {CS-1 / 0.03, CS-2 / 0, CS-3 / 0, CS-4 / 0.01, CS5 / 0.26}.  The degree of confidence for condition state 5 is still the highest but relatively low at 26% (compared to 80% in DS rule). Since the conflict between the data was shifted to ignorance, the ignorance confidence is now 29% (compared to 4% in DS rule). Therefore, these results are still not conclusive and there is the need to involve other attributes for a more reliable decision. 3.4.3 Evaluating an Overall Bridge Condition Index (BCI) The above section detailed how the condition rating for a single index (attribute), namely secondary condition index is determined using two different rules of combination.  In both the operations, the same rules of combination are applied, but what differed is the manner of handling conflict. In order to obtain an overall bridge condition rating, the BPA for each condition index is similarly evaluated by combining the BPA of each parameter with the next level of the hierarchical framework.  As depicted in Figure 3-1, the four condition indices can be written in terms of the parameters identified earlier, as }{ 11neE = ; }{ 22neE = ; }{ 33neE = ; and }{ 44neE = . Similarly, the credibility factors for each parameter are defined as 1λ = {n1λ };  2λ = {n2λ }; 3λ ={n3λ }; and 4λ ={n4λ }. The condition indices can similarly be combined higher-up to obtain the overall condition rating.   70 Subjective judgment plays a crucial role in evaluating bridge condition assessment as demonstrated using appropriate reliability factors. The incipient data reported in Liang (2001) was adopted for this study by referring to the evaluation content and weighting factors only. Conservative reliability factors that were assigned in the current study led to the evaluation of overall bridge condition, primary condition index and secondary condition index, respectively, as 99.90% CS-5 and 99.68% CS-5 and 80.69% CS-5 (CS-5 representing severe damage). In contrast to this, Liang (2001) evaluated the entire Bridge Condition as "Light Anxiety" with no clear indication of the state of primary elements although weighting functions were assigned to individual members. If the reliability factor of all elements were set at a constant say 1.00 (to be consistent with Liang (2001)), using the HER framework, the overall bridge condition, primary condition index and secondary condition index, respectively, evaluated as 71.88% CS-1, 73.81% CS-1 and 51.5% CS-5. Comparing this with the former indices (calculated using conservative reliability factors) one can conclude that the assessment is highly dependent on subjective (expert) input. Further it can be concluded that it can be modeled more systematically using the HER framework by generating multiple condition indices.   Condition assessment requires a rational, repeatable, and transparent approach. Evaluation process for bridge condition rating is a challenging task as it involves aggregation of diverse nature of contributing distress indicators to interpret an overall state of its health. The problem becomes increasingly complex due to uncertainties attributable to inherent subjectivity in the interpretation process. As demonstrated using an example, the hierarchical evidential reasoning  framework proposed for condition assessment of bridges existing bridge data can be adopted for evaluating the condition indices as well as overall condition of the bridge. The HER framework   71 can combine subjective, imprecise and incomplete information, and even conflicting data.  The HER model is based on Dempster-Shafer (DS) rule of combination, which can combine multiple bodies of evidence by incorporating both aleatory (variability, heterogeneity) and epistemic (incertitude, ignorance) uncertainties.   The combination based on Dempster-Shafer rule is more valuable as lesser data is lost during normalization compared to Yager rule where conflict in data is shifted to ignorance. One of the major advantages of using HER is that it has capability to deal with incomplete and conflicting evidence without making strong assumption about missing data as required in other soft computing methods. The HER model can combine multiple bodies of evidence provided they are obtained (or assumed) from independent sources. Because of its robust framework and its firm mathematical foundation, the HER model can be modified at any level of hierarchical structure without changing the recursive combination algorithm.  The basic algorithm used in the proposed model is based on DS rule of combination, which assumes that stochastic independence of sources avoids “conflicts” through normalization process (Marashi and Davis 2006). Many alternatives to this combination rule have been proposed in response to these two issues. To address “conflict” and “normalization”, techniques such as Smets (1990), Inagaki (1991), Murphy (2000), and more recently by Dezert and Smarandache (2004) have been proposed. Marashi and Davis (2006) have also proposed an extension of DS rule to deal with the problem of “dependence” using t-norm based combination rule.    72 Chapter  4: Quality Function Deployment for Infrastructure Management A version of this chapter has been published in the ASCE's Journal of Infrastructure Systems. Bolar, A., Tesfamariam, S., and Sadiq, R. (2014).  "Management of Civil Infrastructure Systems: A QFD-Based Approach." Journal of Infrastructure Systems, 20 (1). doi:10.1061/(ASCE)IS.1943-555X.0000150 4.1 Background An overview of Quality Function Deployment (QFD) and the process of implementing QFD in general were presented in Chapter 2. In this chapter, background for implementing QFD to bridges is provided followed by a case study. Published literature on QFD related to either private or public infrastructure exists, but is not extensive. Na et al. (2011) have presented a decision-making model using QFD for Power Utility Service Improvement.  Partovi (2004) has used QFD for establishing the strategic location of a business facility among various sites. Chen (2011) has adopted fuzzy QFD for knowledge management (KM) implementation in a healthcare institute. While these examples can be categorized as private infrastructure, some literature has been identified relating to public infrastructure. Kabeil (2010) using the analytic hierarchy process (AHP) along with QFD for crisis management. Chen et al. (2011) have published an environmental risk assessment (ERA) model using QFD for the location selection problem of international airports in order to avoid losses due to natural disasters.  Lami and Vitti (2011) have developed a framework using the QFD approach for urban redevelopment projects.  Radharamanan et al. (2008) have performed analysis on the quality of service in an urban transportation system using QFD. Shimazoe et al. (2010) have adopted QFD for identifying errors in configuration of railway signalling systems.     73 While most of the above published literature deals with certain types of infrastructure, not much study has been geared towards public infrastructure management especially in the field of maintenance. In this study, the use of QFD is demonstrated towards including customer concerns in maintenance and rehabilitation/replacement issues of infrastructure. As described in the introduction, bridges have been used as an example though the concepts can be equally applied to other types of infrastructures as well.  The application of QFD for management of bridges is a relatively new concept. The only three references closely related to QFD for bridge maintenance are as follows: • Junhai et al. (2007) describe that portion of Bridge lifecycle design in China is based on QFD. • Malekly et al. (2010) has used QFD in evaluating the conceptual bridge design.  • The European Life-Cycle Management System (LMS) tool LIFECON extensively adopts QFD in Life Cycle Management and is described in detail below: Söderqvist and Vesikari (2003) have reported that sustainability concepts are included in life cycle management of concrete infrastructures within LIFECON. The tool is generic in nature and can therefore be applied to a wide variety of infrastructure ranging from buildings, bridges, and nuclear power plants. The sustainability concepts included are: human requirements, economy, ecology (economy of the nature) and cultural heritage and acceptance. For optimizing and decision-making, the user is provided with a choice of using Quality Function Deployment (QFD), Risk Analysis or Multi Attribute Decision Aid Method (MADA). The use of QFD within LIFECON is for (i) prioritizing alternative maintenance, repair and rehabilitation technologies (MRR); and (ii) evaluating budget sharing between each of the repair strategies. However, Sarja (2004) has also reported the use of QFD within LIFECON in obsolescence analysis integrating sustainability. In other words, obsolescence in the context of LIFECON is the inability to satisfy   74 changing functional (human), economic, cultural or ecological requirements.  Lair (2004) provides detailed information about the use of QFD within LIFECON. Most current maintenance programs address engineering issues by established inspection and maintenance practices. These would normally be under the authority of the owning jurisdiction agency such as Municipal, Provincial, Federal, etc., agencies. However, maintenance programs lack the involvement of consumer demands during maintenance decisions. From an infrastructure owner's perspective, involvement of both engineering and consumer demands in the maintenance program would be compelling, but improve quality and economics by addressing exactly what is essential. Including the voice of consumer would not only be relevant for on-going maintenance, but important especially during decisions that lead to for example replacing a landmark bridge. The use of QFD in decision-making is not limited to making an overall project decision.  For a given infrastructure project, the various disciplines involved can use QFD individually. The end goal of inspection of any infrastructure would enable the decision-maker to undertake specific action based on the findings. For a normal maintenance, the decision can be either "do nothing" or "improvement needed to the structure" in accordance with structural manual if available. In the absence of a structural manual, the responsible engineer may recommend a decision based on engineering analysis and investigation. A non-routine major maintenance may be done for various reasons such as following a seismic event, for assessing an "upgrade" for additional capacity, or to comply with updated code requirements, etc. This maintenance can involve three scenarios for decision-making - "rehabilitate", "replace" or "no action".  As an example for bridge maintenance, decision-making can involve decisions to perform inspections for normal maintenance of bridges or for major decisions involving rehabilitation/ replacement. The decisions for inspection prioritization for example may   75 primarily involve technical personnel whereas a rehabilitation/replacement decision can involve social, economic and other factors as well.  While maintenance programs such as LIFECON do utilize QFD in ranking between alternative MRR strategies and budget sharing, in this study, Quality Function Deployment (QFD) is proposed for infrastructure maintenance by incorporating consumer demands (phrased in QFD as "voice of the customer") (i) Inspection Prioritization (ii) Decision-Making related to Replacement and/or Rehabilitation scenarios. Furthermore, advanced normalization techniques are utilized to give the study a unique dimension.   4.2 Application of QFD in Infrastructure Management 4.2.1 Framework for Infrastructure Inspection Prioritization using QFD Inspecting a structure, whether routine or for evaluating damage can result in valuable information for condition assessment. Technical evaluation of the inspection results aid in ongoing improvements to assure integrity of the structure or lead to major rehabilitation or maintenance.  Ideally, a condition assessment should be classified and evaluated by incorporating uncertainties in order to identify priority (critical) items that need immediate attention (Bolar et al., 2012). While technical input is ineluctable, the inspection prioritization could be more relevant if augmented using input from the customer. In fact, customer satisfaction is apparent in private enterprises; loss of customers would mean lost sales leading to reduced cash-flow for the business. However, for public infrastructure the owner-customer relationship is normally between the government (owner) and customer being the end user of the infrastructure. As such, the relationship holds an intrinsic value but is nevertheless important. Input from citizens can be effectively used to facilitate improvement and change in government culture (Rivenbark and Ballard, 2011). As an example, for bridges, the end user would be mainly the bridge user in the form of a motor driver, pedestrian, etc., although communities and businesses influenced by the bridge also hold stake. Unlike a private enterprise, if a bridge user is   76 unhappy with the bridge he may not have many choices or "shop around" for another bridge. Furthermore, these needs could also be combined with the needs arising from technical concerns due to engineering requirements. QFD can be effectively used to capture all these requirements without losing focus on the customer's needs. A conceptual flow of information using house of qualities is depicted in Figure 4-1.    Figure 4-1 Infrastructure Inspection Prioritization and Maintenance Decision-Making using QFD   77   In order to establish the WHATs, consumer input can always be generated by input from residents, businesses and any other groups affected by the infrastructure modification. Some examples include community engagement meetings, surveys by mail, phone, or emails, inviting focus groups, etc. The WHATs should be based on recommendations from the customer after relevant information is communicated by stakeholders involved in the project. For example, for an infrastructure upgrade, a consumer may wish environmentally friendly materials and construction. However, this may result in cost escalation requiring additional funds that the consumer may not be aware of. The stakeholders could then communicate the options to the customer and open the floor for discussion. The intent should be to capture as much information from the customer without distortion.   Once the WHATs are established the next step would be to evaluate the means to accomplish i.e. the HOWs. The consumer being the end user of the infrastructure would only be interested in items that have an immediate effect on them. For example, a motor driver would naturally be interested in the quality and driving comfort rather than the quality of sub-grade under the road. In order to assure safety and integrity, the WHATs should have relevant engineering involvement. Since the QFD process is only to identify inspection items,  the house of quality has been termed Inspection House of Quality (IHOQ). The simplest way of generating HOWs for the IHOQ would be to adopt inspection items from the inspection manual for the infrastructure if available. If not, relevant engineering assessment could be performed in order to establish the IHOQ HOWs. The intent here should be to identify engineering requirements to implement WHATs. Once the IHOQ is complete, the relationship matrix and the correlation matrices could be completed in order to arrive at the absolute weights and hence the priorities. The priority inspection items could then be augmented with existing inspection schedules or special inspections conducted if critical to the needs of the customer.    78  4.2.2 Framework for Infrastructure Management Decision-Making Using QFD The results from the IHOQ may result in items for a routine maintenance action that may satisfy the customer. However, major damages found during inspection may identify obsolescence of the infrastructure or components.  Significant changes to engineering or environmental regulations, or additional demands placed on the structure may require an upgrade or retrofit.  This may lead to cases where a decision requiring either rehabilitation or replacement of the structure is made.  In order to have continued customer involvement HOQs solely related to rehabilitation and replacement could be established as shown in Figure 4-1 and is defined below: Rehabilitation House of Quality (REH-HOQ): A house of quality for evaluating consumer attitude towards decisions that may lead to rehabilitation of the infrastructure. Similar to the IHOQ, the WHATs in the REH-HOQ are consumer input established after active communication with the consumers. The HOWs are identified in order to ascertain ways in which the WHAT can beestablished. However, the WHATs need not be limited to technical issues alone, but any category that could affect decision-making such as economic, social, environmental, etc., issues.  Replacement House of Quality (REP-HOQ): A house of quality for evaluating consumer attitude towards decisions that may lead to replacement of the infrastructure. This HOQ is similar to the REH-HOQ except that the intent here is to identify replacement related issues of the infrastructure. 4.3 Bridge Inspection Prioritization using Quality Function Deployment  As stated in the previous sections, although the concepts described in this study are applicable to any  infrastructure type, in order to demonstrate the application of QFD, bridges have been chosen as an example. For the HOW items of the IHOQ, inspection items from the Colorado Department of   79 Transportation (CDOT) Pontis Bridge Inspection Coding Guide were adopted. Table 4-1 presents a hypothetical survey for routine bridge maintenance.  Survey terms that are not self-explanatory are elaborated under the remarks section of the table. The survey items are categorized and the intent of the questions is described as follows: Riding Comfort:  For evaluating whether the bridge user finds the ride comfortable, and can identify the items that needs improvement. Safety: For determining whether the user is finding the bridge safe during use. Economy: Intended to determine whether funding of the maintenance actions economical. The percentage of budget amounts shown is assumed.  Environment: Intended for identifying if the consumer values environmentally friendly materials and actions for maintenance.  Table 2-5 scales have been adopted for developing WHATs for the inspection prioritization portion of this study. The responses to the questions are obtained on a scale of 1 (Very Unsatisfied) to 9 (Extremely Satisfied) and is depicted in Table 4-4. 4.3.1 HOWs and WHATs  The items (questions) listed in Table 4-1 form a set of customer-requirements or WHATs.  As described in the previous section, the means of achieving each of these WHATs i.e. the HOWs is identified by comparing the WHATs to inspection items in the Colorado Department of  Transportation (CDOT) Pontis Bridge Inspection Coding Guide shown in Table 4-2. The comparison is described in Table 4-1 under the remarks column. The response ratings to the questions are adopted as the relative importance rating of the IHOQ.    80 Table 4-1 Relating Hypothetical Survey to Pontis® Elements Consumer Survey Questions Response5 Pontis®Element for use as HOWs   Explanation Riding Comfort Traction on Road Surface 7 Deck or Deck Slab (With or without overlay); Approach Slab Traction of road could be low due to various reasons (such as re-surfacing required). Condition of road surface during rainy and winter days could be improved by adequate drainage, etc. Frequent potholes if reported by users may need further investigation to find the cause. For all these items Approach Slab and Deck slabs would be areas of immediate interest.  Condition of  Road Surface - Rainy Days 9 Deck or Deck Slab (With or without overlay); Approach Slab Condition of  Road Surface - Winter  3 Deck or Deck Slab (With or without overlay); Approach Slab Number of Potholes 4 Deck or Deck Slab (With or without overlay); Approach Slab Aesthetic Condition 8 Any visible element such as Paint, Flag/Pole, Sidewalks, Railings, Culverts, Wingwalls If bridge users notice degrading aesthetic condition such as peeling paint (or a different colour suggested), condition of sidewalks, wingwalls, etc the concerns could be investigated during inspection. Safety Visibility of Traffic Signs  9 Flag/Pole If traffic sign visibility problems are reported the relevant flag/pole Pontis®Element could be visited Approach (Ahead) Visibility or hinderance 7 Approach Roadway Alignment; Superstructure If approach alignment issues are reported by users, an inspection could be carried out.  Pedestrian Safety 9 Railing, Sidewalks and Flag/Pole Pedestrians may report safety issues such as failed handrails, deficient sidewalks, fallen traffic signs, etc., that may warrant inspection  Countermeasures for Threat/Natural Disasters  7 Superstructure, Substructure This being an extreme event requiring such as seismic retrofit primary elements such as superstructure and substructure would be areas requiring immediate attention Feel of Vibration/Movement 7 Superstructure, Substructure, Joints and Bearings If the users report excessive vibration/movement, inspection of joints, bearings as well as superstructure/substructure may be required Economy 25% Budget Amount Spent on Surface Maintenance 7 Deck or Deck Slab (With or without overlay); Approach Slab If the bridge user indicates the budget needs to be re-allocated the economics may need to be justified by inspection results. For example, if the user recommends more money to be spent on pothole  20% Budget Spent on Pothole Repairs  7 Deck or Deck Slab (With or without overlay); Approach Slab 5% Budget Spent on Aesthetics 5 Any visible element such as Paint, Flag/Pole, Sidewalks, Railings, Culverts, Wingwalls repairs than aesthetics, a process could be initiated to re-allocate resources or obtain additional fundings.                                                  5 Very Unsatisfied (1) to Extremely Satisfied (9)   81 Table 4-1 Relating Hypothetical Survey to Pontis® Elements (continued) Consumer Survey Questions Response6 Pontis®Element for use as HOWs   Explanation 40% Budget Amount Spent on Structural Maintenance 9 Superstructure, Substructure, Joints and Bearings  10% Budget Amount Spent on Countermeasures for Vulnerability 9 Superstructure, Substructure Environment Use of Green (Environmentally Friendly) Products and Procedures 5 Paint/Coatings, Sidewalks, Deck If the user survey indicates an interest towards environmentally friendly products, items during maintenance such as deficient paints/coatings, overlay, sidewalks could be rehabilitated with environmentally sound materials or construction.                                                     6 Very Unsatisfied (1) to Extremely Satisfied (9)   82 Table 4-2  Colorado Department of Transportation (CDOT) Pontis® Elements  Designation Material/Description Pontis® Element Index Deck (with or without overlay) Concrete, Steel, Composite, Timber, Railroad 12, 13, 14, 18, 22, 23*, 24*, 25*, 26, 27, 28, 29, 30, 31, 32, 35*, 36*, 54, 55, 60* Deck Slab (with or without overlay) Concrete Slab 38, 39, 40, 44, 48, 52, 53 Super Structure Concrete, Steel, Timber, Other (Masonry) 101 - 161 Substructure Concrete, Steel, Timber, Other (Masonry) 201 - 235 Culverts Steel, Concrete, Timber, Other 240 - 243 Joints Expansion, Seal, Elastomeric, Construction 300-304; 305*-308* Bearings Elastomeric, Moveable, Fixed 309*-315 Approach Slab Pre-stressed or normal concrete 320, 321 Wing Walls Slope Protection, Berms, etc. 326*, 327* Railing Concrete, Timber, Metal, Misc 330 - 335* Sidewalks Metal , Concrete, Timber 336* - 339* Paint/Coatings Concrete 340*, 341* Scour  361 Flag/Pole Sign Attachment to Bridge 342*, 343* Approach Roadway Alignment  520* Channel/ General Channel, Bank, Debris, Waterway Adequacy,  501*, 502*, 504*, 505*, 510*   83 Table 4-3 Priority Ranking of Pontis® Inspection Items Using House of Quality Absolute Weights  Pontis® Inspection Items Overlay Deck Superstructure Substructure Wingwalls Paint on Steel Alkali-Silica Reaction (ASR) Scour Approach Alignment Bearings Approach Slabs Expansion Joints Culverts Curbs/Sidewalks Concrete Surface Coatings Bridge Handrail Sign Attachment to Bridge  Absolute Weight Evaluation Technique                   Independent Scoring Method  3 8 11 11 13 1 6 14 15 17 4 10 16 5 1 7 9 Lyman's Normalization  16 12 3 3 7 14 17 13 1 11 10 9 2 8 14 6 5 Wasserman's Normalization  1 3 7 4 9 2 8 12 16 13 15 17 5 6 10 14 11   84 Table 4-4 WHATs vs. HOWs Correlation Scale  STRONG    WEAK Value 9 7 5 3 1 Relationship Extremely Strong Moderate Weak Extremely 4.3.2 Relationship Matrix For each of the WHATs, relationships if a HOW could accomplish a WHAT were determined by subjective judgment using a 5 tier scale. Table 4-4 shows the scale adopted to establish the relationship between each HOW and WHAT.  A 5 tier scale is used starting from 1 through 9, where 1 represents weak relationship and 9 represents strong relationship. Figure 4-2 shows the completed QFD relationship matrix for Wasserman's normalization case. For example, the WHAT "Traction on Road Surface" is assigned a strong relationship 9 with "overlay", whereas "number of potholes" has been assigned a zero relationship with "Bridge handrail" as the presence of potholes and condition of handrails are un-related. 4.3.3 Correlation Matrix The correlations between each of the HOWs (HOW vs.HOW) are represented in the roof of the House of Quality using a 3-tier scale ranging from 0 to 1, where weak is 0.1, medium 0.3 and strong 0.9. Referring to Figure 4-2, the correlation between substructure and scour that would be strongly correlated is assigned 0.9, whereas correlation between wingwalls and deck is assigned weak correlation 0.1.    85   Figure 4-2 Inspection HOQ for Inspection Prioritization - Wasserman's Normalization Relative ImportanceTraction of Road Surface 7Condition of Road Surface - Rainy Days 9Condition of Road Surface - Winter 3Number of Potholes 4Aesthetic Condition 8Visibility of Traffic Signs 9Approach (Ahead) Visibility 7Pedestrian Safety 9Countermeasures for Threat/Natural Disasters 7Feel of Vibration/Movement 725% Budget Amount Spent on Surface Maintenance 720% Budget Spent on Pothole Repairs 75%  Budget Spent on Aesthetics 540% Budget Amount Spent on Structural Maintenance 99Use of Green (Environmentally Friendly) Products 5Use of Green (Environmentally Friendly) Procedures 5Absolute Weight:RANK:10% Budget Amount Spent on Contermeasures for Vulnerability0.95.3 4.6 4.9 6.0 3.5 5.8 3.7 3.40.30.1 0.3 0.1 0.10.10.90.11.9 2.4 2.3 1.4 1.3 2.0 1.1 1.0 0.90.1 0.10.10.10.1 0.10.10.1 0.1 0.9 0.10.30.10.1 0.1 0.3 0.10.10.3 0.1 0.10.9 0.1 0.10.10.3 0.30.1 0.9 0.10.90.30.1 0.10.1 0.10.1 0.1 0.9 0.1 0.10.9 0.3 0.9 0.1 0.10.10.30.1 0.10.1 0.10.10.1 0.1 0.10.90.90.1 0.9 0.1 0.1 0.1 0.1 0.1 0.10.30.9 0.10.3 0.1 0.1 0.3 0.10.9 0.1 0.10.9 0.1 0.10.1 0.1 0.1 0.1 0.1 0.10.90.1 0.9 0.1 0.1 0.1 0.10.1 0.1 0.3 0.10.1 0.1 0.1 0.1 0.1 0.1 0.9 0.1 0.10.3 0.9 0.1 0.1 0.1 0.1 0.10.1 0.3 0.1 0.3 0.3 0.9 0.1 0.10.90.9 0.9 0.9 0.9 0.9 0.90.9 0.9 0.9 0.9 0.90.30.9 0.9 0.9 0.9 0.9 0.90.3 0.9 0.9 0.39500.0960.057Sign Attachment to Bridge0030997977Bridge Handrail000097579903597Curbs/Sidewalks05507007070.0980.093 0.1065Culverts00005007 7 005Tunnel Lining970.057000.0577350.052037300Bearings000039033097Expansion Joints05Approach Slabs9999009000.0570.057Apporoach Alignment0000059000Scour0000909Wingwalls00070Alkali-Silica Reaction (ASR)95799000900799009 99 99 003705057090.1220.203Superstructure000030.0760730 03 90 0370.081090.0860.101 0.08 0.135 0.09 0.056Substructure0000307707050.0860.1270Paint/Coatings97Overlay9999900Deck353700.193 0.124 0.0859 9 09 0 39 7 030.18 0.124 0.094030.089 0.077 0.121 0.086 0.058 0.058 0.058 0.058 0.056 0.103 0.112 0.106 0.062 0.090.056 0.056 0.056 0.053 0.085 0.116 0.111 0.064 0.080.115 0.096 0.093 0.101 0.049 0.089 0.05 0.077 0.045 0.051 0.065 0.04 0.093 0.074 0.046 0.046 0.0890.053 0.053 0.053 0.048 0.084 0.112 0.093 0.054 0.0870.1870.029 0.288 0.082 0.062 0.026 0.0160.078 0.101 0.026 0.026 0.147 0.049 0.147 0.0160.115 0.091 0.099 0.075 0.135 0.094 0.0530.016 00.125 0.061 0.065 0.1 0.101 0.1 0.0480.087 0.076 0.055 0.086 0.101 0.101 0.093 0.0760.1720.023 0.029 0.007 0.012 0.056 0.044 0.082 0.024 0.0640.05 0.062 0.115 0.127 0.04 0.084 0.038 0.053 0.0250.048 0.043 0.043 0.044 0.12 0.095 0.089 0.053 0.0790.031 0.05 0.079 0.059 0.065 0.0280.053 0.045 0.018 0.043 0.054 0.04 0.013 0.0070.079 0.12 0.086 0.053 0.0790.09 0.093 0.083 0.14 0.055 0.143 0.06 0.0580.178 0.116 0.094 0.099 0.071 0.13 0.096 0.050.037 0.054 0.0411 3 7 4 90.05 0.05 0.05 0.0460.179 0.135 0.105 0.1 0.085 0.155 0.1 0.060.051 0.065 0.040.06 0.06 0.06 0.0615 12 10 11 9 13 9 7 50.115 0.096 0.093 0.101 0.049 0.089 0.05 0.077 0.0455 5 40.096 0.082 0.087 0.116 0.067 0.114 0.072 0.066 0.03 0.042 0.036 0.0180.05 0.062 0.115 0.127 0.04 0.084 0.038 0.053 0.0252 8 12 16 13 15 17 5 6 10 1410 8 5 70.104 0.138 0.109 0.065 0.0550.081110.034 0.058 0.045 0.038 0.0560.093 0.074 0.046 0.046 0.0891109 0 00 0 9 0 0 5 9 0 00 3 5 7 9 9 97 5 5 70 0 0 9 0 0 05 9 9 7 0 0 09 9 9 7 7 7 9 9 7 9 3 00 39 7 3 3 3 9 9 7 0 5 5 5 0 7 9 7 30 0 3 7 500 5 5 5 0 7 9 7 39 7 3 3 3 9 9 70.053 0.045 0.018 0.043 0.054 0.04 0.013 0.0070.128 0.098 0.081 0.109 0.056 0.118 0.069 0.07 0.043 0.049 0.047 0.037 0.072 0.088 0.06 0.0540.049 0.047 0.037 0.072 0.088 0.06 0.054 0.0810.128 0.098 0.081 0.109 0.056 0.118 0.069 0.07 0.043CONSUMER WHATsENGINEERING HOWs  86 4.3.4 Discussion  The absolute weights of the IHOQs were generated for each of the normalization cases described in this study namely Independent scoring, Lyman's normalization and Wasserman's normalization techniques. Table 4-3 presents the absolute weight ranking obtained using each of these methods. Paint on steel and concrete surface coatings are obtained as a priority using the independent scoring method. However, since this method can assign a weak relationship when a WHAT is related to two more HOWs, the results are not very reliable. Approach alignment inspection is ranked first using the Lyman's normalization. Although this method deals with the drawbacks of independent scoring no dependencies between the items of the correlation matrix is considered. Wasserman's normalization provides overlay inspection as a critical item. This method can deal with the drawbacks of both independent scoring and Lyman's normalization and the results can therefore be considered more reliable. 4.4 Bridge Maintenance Management using QFD Any decision-making process for structural maintenance can broadly result in three scenarios - repair/rehabilitation (including partial replacement), complete replacement or a "No Action" required scenario. The items leading to these scenarios can involve complex assessments, technical investigations, preliminary engineering designs and most importantly community hearings or surveys conducted by municipalities or agencies that possess ownership of the entity. These surveys including any other investigations, etc., can be included in the HOQ for implementing the QFD approach. The QFD approach for bridge maintenance decision-making is demonstrated in this thesis using customer survey data for Johnson Street Bridge in the city of Victoria, BC, Canada. All data used in this study was available at http://www.johnsonstreetbridge.com/. The Johnson Street Bridge is a Bascule-type bridge with a counter-weight at one end facilitating the lowering of the opposite end.   87 The bridge has two separate Bascules, the Railway section and the Highway section and was designed under the direction of Mr. F.M. Preston, City Engineer in 1920 (http://www.johnsonstreetbridge.com/the-project/history/ [Accessed 23 Jan 2012]). The main opening span is 148 feet in length and is balanced over a 45-foot fixed span when open. The eastern approach has a 110’ fixed girder while the western approach has a 73’ fixed girder. The counter weight block on the highway span is a hollow concrete structure consisting of a number of smaller concrete weights and tips the scale at over 780-tons. It balances the 350-ton opening span. The original Johnson Street Bridge opened in the year 1924 had a timber deck that eventually absorbed water and led to increase in weight causing machinery operation problems. By 1966, the timber deck was replaced by an open steel grid decking of constant weight. In 1979, extensive corrosion–related repairs were made to the superstructure. In April 2009, the results of an overall condition assessment of the Johnson Street Bridge identified extensive corrosion in steel structural beams, obsolete instrumentation and significant seismic vulnerability. The comprehensive review concluded that substantial investment would be required by 2012 to avoid further deterioration, increasing operational costs and possible closure. The Victoria city council decided to replace the bridge after considering many factors including safety, accessibility, improved pedestrian and cycling amenities, heritage values, sustainability and traffic and business disruption as well as an extensive engagement process (http://www.johnsonstreetbridge.com/the-project/overview-2/ [Accessed 23 Jan 2012]).  WHATs: The Victoria City Council decided to borrow $49.2 million to replace the Johnson Street Bridge after reviewing the results of extensive public consultation including emails, personal contact with citizens during open houses, at local markets and at the bridge (reference). In addition representative surveys, for businesses in downtown Victoria and the residents of Victoria, were conducted. The input from citizens (or voice of the citizen/customer in QFD terms) is defined as a   88 consumer WHAT in this study. The consumer can be either a resident citizen or a stakeholder such as a business entity. As such the surveys conducted included: • Representative survey of businesses in Downtown Victoria and Victoria West (http://www.johnsonstreetbridge.com/wp-content/uploads/2010/05/JSB-Business-Presentation.pdf [Accessed 23 Jan 2012]);  • Representative survey of residents of Victoria and 2600 (including mail-in surveys) (http://www.johnsonstreetbridge.com/wp-content/uploads/2010/05/JSB-Residential-Presentation.pdf [Accessed 23 Jan 2012]). HOWs: Had QFD been implemented for the Johnson Street Bridge each of the consumer WHATs would have been thoroughly investigated by a team consisting of the survey participants, stakeholders, engineers or anyone deemed to be affected by modifications to the bridge. While in an actual QFD, establishing the HOWs would be result of a brainstorming process, the criteria for establishing the HOWs is presented in Table 4-5. The 5 tier scale shown in Table 2-5 is used. Figure 4-3 to 1-7 show the completed QFD relationship matrix for independent scoring, Lyman's normalization and Wasserman's normalization, respectively. For example, referring to Figure 4-3, the WHAT "replacement cost related issues" was assigned an extremely strong relationship 9 with "increasing taxes", "borrowing money", and for "toll" (all directly related to cost). However, strong relationship 7 was assigned to the same items under "replacement construction related issues" assuming that construction related issues would be more technical in nature, but nevertheless could impact cost and therefore would exhibit a strong relationship.    89 Table 4-5 Johnson Bridge QFD Decision-Making Scenarios ― Description of HOWs HOW Description related to the Bridge Economic Factors Increase Taxes How would an "increase in taxes" correlate with each of the WHATs Borrowing How would "borrowing" funds correlate with each of the WHATs Toll How would establishing a "toll" correlate with each of the WHATs Social Factors Customer Satisfaction How would simply accepting the requirement for customer satisfaction correlate with each of the WHATs Aesthetics How would Aesthetic value correlate with each of the WHATs Heritage Value How would Heritage value correlate with each of the WHATs Safety Driven Traffic Signs How would improved "traffic signs" correlate with each of the WHATs Visibility How would improved "visibility" correlate with each of the WHATs Safety during Maintenance How would improved "safety during maintenance" (For e.g. additional measures during replacement) correlate with each of the WHATs Pedestrian Safety How would improved "pedestrian safety" correlate with each of the WHATs  Technical Factors Technical Investigation How would conducting a "technical investigation" correlate with each of the WHATs Vibration/Movement How would limiting vibration/movement correlate with each of the WHATs Seismic Counter-measures How would improved "seismic counter-measures" correlate with each of the WHATs Maintenance Efficiency Related Improved Access How would "improved access" after maintenance correlate with each of the WHATs Uneven Surface How would improved riding surface characteristics correlate with each of the WHATs No Potholes How would absence of "pot-holes" correlate with each of the WHATs Environmental Factors: Green Products, design/construction How would use of green products, design or construction correlate with each of the WHATs      90  Figure 4-3 Typical HOQ for Johnson Bridge using Independent Scoring: Rehabilitation Option - Residents Response (RehR)  EconomicSocialSafetyTechnicalMaintenance EfficiencyEnvironmental` `Relative Importance52361512118754433331Absolute Weight:Combined Absolute Weight (SCORE):Replace as old bridge will need to be replaced eventuallyReplace as old bridge is in poor conditionReplace as Heritage value not importantReplacement would provide better pedestrian accessReplacement would be modernDon't know if replacement should be doneReplacement Cost related issues Replacement Construction related issuesReplace just to have a new bridgeReplacement will last longer/ long term solutionReplacement would look better/ more attractiveReplacement for Traffic efficiency related issuesReplacement for Maintenance related issuesReplacement would be saferReplacement would provide better bicycle access0.30.3 0.30.3 0.3 0.30.30.3 0.3 0.3 0.3 0.30.3 0.3 0.3 0.30.3 0.3 0.3 0.30.90.3 0.3 0.3 0.3 0.9 0.9 0.90.90.3 0.3 0.3 0.3 0.6 0.90.90.3 0.3 0.3 0.3 0.9 0.9 0.9 0.9 0.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.9 1.00.3 0.3 0.3 0.3 0.6 0.9 0.9 0.9 0.9 0.9 0.30.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.9 0.9 0.3 0.90.3 0.3 0.3 0.3 0.9 0.9 0.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.90.9 0.9 0.9 0.9 0.3 0.90.3 0.3 0.9 0.9 0.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.30.3 0.3 0.3 0.3 0.3 0.90.9 0.9 0.9 0.9 0.9 0.30.9 0.9 0.3 0.90.9 0.9 0.3 0.3 0.9 0.90.9 0.9 0.9 0.9 0.3 0.90.9 0.9 0.3 0.9 0.90.9 0.9 0.9 0.3 0.90.9 0.9 0.9 0.9 0.0 0.90.91.0 1.0 1.0 1.0 1.0 1.0 1.0 1.00.9 0.9 0.9 0.3 0.9 0.90.9 0.9 0.9 0.9 0.9 0.31.0 1.0 1.0 1.0 1.07.6 8.2 8.2 7.6 10.01.0 1.0 1.0 1.0 1.0 1.013.0 12.815.4 13.3 11.2 13.6 13.3Increase TaxesBorrowingTollCustomer SatisfactionAestheticsHeritage ValueTraffic Signs13.614.8 14.8 14.2 14.2 13.7 9.7No PotholesGreen ProductsGreen DesignGreen ConstructionVisibilitySafety during MaintenancePedestrian SafetyTechnical InvestigationVibration/MovementSeismic Couter-measures9 7 7REPLACEMENT3 3 3Improved AccessUneven Surface57 7 7 5 1 1 0 70 1 0 1 177 77 7 7 7 7 9 5 77 7 7 7 5 77 0 5 0 1 79 95 5 5 57 7 7 7 10 5 9 7 7 50 01 1 0 0 0 077 7 7 77 7 7 7 90 7 7 7 7 75 53 5 5 5 55 5 7 3 3 9 733 0 3 0 3 35 5 1 1 17 7 7 7 00 5 7 7 7 71 13 3 3 3 157 7 7 5 0 5 370 5 3 3 5 71 1 1 1 17 7 7 7 09 7 7 7 7 19 99 9 9 9 977 7 7 0 5 0 370 7 0 0 7 09 9 9 9 97 7 7 7 70 3 7 7 9 97 77 7 7 7 777 7 9 7 9 0 775 7 7 7 7 79 9 9 9 97 7 7 7 70 7 7 9 9 99 97 9 9 9 977 9 9 9 7 777 9 9 9 9 79 9 9 9 91250 1250 1250 1150 8817 7 7 7 7 99 7 0 3 3 37 7877 87722 17 12 18 16 151034 1022 939 923 819 877972 409 838 135 604 10721 1 1 13 7 7 7 1 1CONSUMER WHATsIMPLEMENTATION HOWs  91  Figure 4-4 Typical HOQ for Johnson Bridge using Lyman's Normalization: Rehabilitation Option - Business Response (RehB)  EconomicSocialSafetyTechnologicalMaintenance EfficiencyEnvironmental` `Relative Importance43402119156134Absolute Weight (AW):Combined AW (SCORE):Rehabilitate for Cost related issues Rehabilitate for Heritage related issuesRehabilitate for Construction relatedReplacement not requiredRehabilitation budget is inflatedNeeds to be updatedOtherDon't know0.30.3 0.30.3 0.3 0.30.30.3 0.3 0.3 0.3 0.30.3 0.3 0.3 0.30.3 0.3 0.3 0.30.90.3 0.3 0.3 0.3 0.9 0.9 0.90.90.3 0.3 0.3 0.3 0.6 0.90.90.3 0.3 0.3 0.3 0.9 0.9 0.9 0.9 0.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.9 1.00.3 0.3 0.3 0.3 0.6 0.9 0.9 0.9 0.9 0.9 0.30.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.9 0.9 0.3 0.90.3 0.3 0.3 0.3 0.9 0.9 0.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.90.9 0.9 0.9 0.9 0.3 0.90.3 0.3 0.9 0.9 0.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.30.3 0.3 0.3 0.3 0.3 0.90.9 0.9 0.9 0.9 0.9 0.30.9 0.9 0.3 0.90.9 0.9 0.3 0.3 0.9 0.90.9 0.9 0.9 0.9 0.3 0.90.9 0.9 0.3 0.9 0.90.9 0.9 0.9 0.3 0.90.9 0.9 0.9 0.9 0.0 0.90.91.0 1.0 1.0 1.0 1.0 1.0 1.0 1.00.9 0.9 0.9 0.3 0.9 0.90.9 0.9 0.9 0.9 0.9 0.31.0 1.014.8 14.8 14.2 14.2 13.7 9.71.07.6 8.2 8.2 7.6 10.01.0 1.0 1.0 1.0 1.0 1.0Green ConstructionVisibilitySafety during MaintenancePedestrian SafetyTechnical InvestigationVibration/MovementSeismic Couter-measures13.0 12.813.6 15.4 13.3 11.2 13.6 13.31.0 1.09 7 7REHABILITATIONImproved AccessUneven SurfaceNo PotholesGreen ProductsGreen DesignIncrease TaxesBorrowingTollCustomer SatisfactionAestheticsHeritage ValueTraffic Signs55 5 57 7 759 9 9 7 3 9 0 57 5 5 5 5 57 0 7 0 5 79 95 57 7 7 7 70 1 5 7 5 55 55 55 7 77 7 5 59 5 7 0 5 97 7 7 7 79 9 9 7 57 7 9 7 7 79 95 5 5 5 97 77 7 7 7 775 0 3 0 1 79 9 95 5 5 5 57 7 7 9 9 95 55 5 5 5 57 7 755 5 5 5 5 59 913 3 7 7 7 14.2 4.3 4.3 3.66 4.361 1 1 13 3 3 9 7 0 3 34.645.65 5.31 5.57 5.88 5.75 3.9 4.7114 15 25 15 16 164.83 5.14 4.76 5.2 4.8 4.75CONSUMER WHATsIMPLEMENTATION HOWs  92   Figure 4-5 Typical HOQ for Johnson Bridge using Wasserman's Normalization: Replacement Option - Resident's Response (Rep) EconomicSocialSafetyTechnicalMaintenance EfficiencyEnvironmental` `Relative ImportanceReplacement Cost related issues 52Replacement Construction related issues 36Replace just to have a new bridge 15Replacement will last longer/ long term solution 12Replacement would look better/ more attractive 11Replacement for Traffic efficiency related issues 8Replacement for Maintenance related issues 7Replacement would be safer 5Replacement would provide better bicycle access 4Replace as old bridge will need to be replaced eventually 4Replace as old bridge is in poor condition 3Replace as Heritage value not important 3Replacement would provide better pedestrian access 3Replacement would be modern 3Don't know if replacement should be done 1Absolute Weight:Combined Absolute Weight (SCORE):0.06 0.06 0.06 0.051 1 10.03 0.04 0.04 0.04 0.05 0.063 7 7 7 1 19 7 0 3 3 30.06 0.070.0724 25 38 27 32 388.50 8.43 9.50 11.21 11.54 12.379.95 9.87 9.26 9.18 9.24 9.960.07 0.07 0.076.64 8.79 8.79 7.75 7.610.06 0.06 0.06 0.05 0.05 0.0612.74 13.360.05 0.06 0.07 0.07 0.07 0.080.06 0.060.03 0.04 0.04 0.04 0.05 0.06 0.06 0.060.050.06 0.06 0.06 0.06 0.06 0.060.07 0.07 0.07 0.07 0.080.03 0.04 0.04 0.04 0.040.06 0.06 0.06 0.05 0.05 0.060.07 0.070.05 0.06 0.06 0.06 0.070.03 0.05 0.05 0.04 0.04 0.06 0.06 0.060.050.06 0.06 0.06 0.06 0.06 0.060.07 0.07 0.07 0.08 0.080.03 0.04 0.04 0.04 0.040.06 0.06 0.06 0.05 0.05 0.060.07 0.070.05 0.06 0.06 0.07 0.070.03 0.05 0.05 0.05 0.04 0.06 0.06 0.060.060.05 0.06 0.05 0.05 0.06 0.050.06 0.07 0.07 0.08 0.070.03 0.05 0.05 0.05 0.040.06 0.06 0.06 0.05 0.05 0.060.07 0.080.06 0.05 0.07 0.07 0.070.04 0.05 0.05 0.04 0.04 0.06 0.06 0.060.050.06 0.06 0.06 0.06 0.06 0.060.07 0.06 0.06 0.07 0.080.04 0.05 0.05 0.05 0.040.06 0.06 0.06 0.05 0.05 0.060.08 0.080.05 0.05 0.07 0.07 0.070.03 0.04 0.04 0.04 0.04 0.06 0.06 0.060.050.06 0.06 0.05 0.05 0.05 0.060.06 0.06 0.07 0.08 0.080.04 0.06 0.06 0.05 0.050.06 0.06 0.06 0.05 0.05 0.050.08 0.080.05 0.06 0.07 0.08 0.080.04 0.05 0.05 0.04 0.04 0.06 0.06 0.060.050.05 0.05 0.05 0.05 0.05 0.050.07 0.07 0.07 0.07 0.080.06 0.07 0.07 0.06 0.050.06 0.06 0.06 0.05 0.05 0.060.08 0.090.05 0.05 0.07 0.08 0.090.04 0.04 0.04 0.04 0.05 0.06 0.06 0.060.050.06 0.06 0.05 0.05 0.05 0.069 9 9 9 90.04 0.05 0.05 0.05 0.057 7 7 7 7 90.08 0.080.05 0.06 0.07 0.07 0.0817 7 7 9 9 9 7 777 9 9 9 9 79 9 9 9 97 7 7 7 70 7 7 9 9 99 97 9 9 9 97 7 7 9 7 9 0 775 7 7 7 7 79 9 9 9 97 7 7 7 70 3 7 7 9 97 77 7 7 7 77 7 7 7 0 5 0 370 7 0 0 7 01 1 1 1 17 7 7 7 09 7 7 7 7 19 99 9 9 9 97 7 7 7 5 0 5 370 5 3 3 5 75 5 1 1 17 7 7 7 00 5 7 7 7 71 13 3 3 3 15 5 5 7 3 3 9 733 0 3 0 3 37 7 7 77 7 7 7 90 7 7 7 7 75 53 5 5 5 55 5 5 57 7 7 7 10 5 9 7 7 50 01 1 0 0 0 077 77 7 7 7 7 9 5 77 7 7 7 5 77 0 5 0 1 79 9 9 7 7REPLACEMENT3 3 3Improved AccessUneven Surface57 7 7 5 1 1 0 70 1 0 1 17No PotholesGreen ProductsGreen DesignGreen ConstructionVisibilitySafety during MaintenancePedestrian SafetyTechnical InvestigationVibration/MovementSeismic Couter-measuresIncrease TaxesBorrowingTollCustomer Satisfaction/ Change overAestheticsHeritage ValueTraffic Signs13.614.8 14.8 14.2 14.2 13.7 9.71.0 1.0 1.07.6 8.2 8.2 7.6 10.01.0 1.0 1.0 1.0 1.0 1.013.0 12.815.4 13.3 11.2 13.6 13.30.91.0 1.0 1.0 1.0 1.0 1.0 1.0 1.00.9 0.9 0.9 0.3 0.9 0.90.9 0.9 0.9 0.9 0.9 0.31.0 1.00.90.9 0.9 0.9 0.3 0.90.9 0.9 0.9 0.9 0.0 0.90.90.9 0.9 0.3 0.3 0.9 0.90.9 0.9 0.9 0.9 0.3 0.90.9 0.9 0.3 0.90.30.3 0.3 0.3 0.3 0.3 0.90.9 0.9 0.9 0.9 0.9 0.30.9 0.9 0.30.3 0.9 0.9 0.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.90.90.3 0.3 0.3 0.3 0.9 0.9 0.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.90.9 0.9 0.9 0.9 0.3 0.90.30.30.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.9 0.9 0.31.00.3 0.3 0.3 0.3 0.6 0.9 0.9 0.9 0.9 0.90.90.3 0.3 0.3 0.3 0.3 0.9 0.9 0.9 0.90.90.3 0.3 0.3 0.3 0.9 0.9 0.9 0.90.90.3 0.3 0.3 0.3 0.9 0.9 0.90.90.3 0.3 0.3 0.3 0.6 0.90.30.3 0.30.3 0.3 0.30.30.3 0.3 0.3 0.3 0.30.3 0.3 0.3 0.30.3 0.3 0.3 0.3CONSUMER WHATsIMPLEMENTATION HOWs  93 Correlations are also established between each of the HOWs and are represented in the roof of the HOQ.  Similar to previous cases, these correlations are established on a 3-tier scale. The case study data adopted for this research had survey data for four categories: a) Replacement Option - Resident's Response (Abbreviated as RepR) b) Rehabilitation Option - Resident's Response (Abbreviated as RehR) c) Replacement Option - Business's Response (Abbreviated as RepB) d) Rehabilitation Option - Business's Response (Abbreviated as RehB) The HOQ was generated for each of the above cases. The absolute weight was obtained for each of the HOWs using the HOQ and a combined absolute weight (score) was evaluated for each of the broader headings namely Economic Factors, Social Factors, Safety Driven, Technical Factors, Maintenance Efficiency and Environmental Factors. The HOQs are shown for two cases in Figure 4-3 to Figure 4-7. The results are plotted as pie-charts in Figure 4-6 to Figure 4-8 and are also summarized in Table 4-6, Table 4-7, and Table 4-8. The independent scoring method (Table 4-6) show a higher score towards economic factors - RepR (22%), RehR (24%), RepB (22%), RehB (22%) and resulted in either replacement or rehabilitation i.e. no preference. This could lead to a decision for either replacement, or rehabilitation, or perhaps a combination of both. The Lyman's normalization referring to Table 4-7 showed higher scores towards social issues - RepR (19%), RehR (20%), RepB (21%) and safety – RehB (25%). Rehabilitation resulted as the preferred option. The Wasserman's normalization (Table 4-8) showed higher scores towards environmental issues - RepR (38%), RehR (31%), RepB (46%), RehB (37%), and safety –  RepR (38%), RepB (46%), and RehB (37%). Replacement was the preferred option.    94  Figure 4-6 Independent Scoring Results:  HOQ for Johnson Bridge using: Rehabilitation Option - Residents Response (RehR)  Figure 4-7 Lyman's Normalization Results: HOQ for Johnson Bridge using Rehabilitation Option - Business Response (RehB)  Figure 4-8 Wasserman's Normalization Results:  HOQ for Johnson Bridge using: Replacement Option - Resident's Response (RepR)  Economic, 24Social, 19Safety, 12Technical, 17Maintenance Efficiency, 14Environmental, 14Economic, 14Social, 15Safety, 25Technological, 15Maintenance Efficiency, 16Environmental, 16Economic, 24Social, 25Safety, 38Technical, 27Maintenance Efficiency, 32Environmental, 38  95 Table 4-6 Results from HOQ for Johnson Bridge - Independent Scoring Method  Residential HOQ Business HOQ  Replacement Rehabilitation Replacement Rehabilitation Economic 22 24 22 22 Social 17 19 18 18 Safety 12 12 13 12 Technical 18 17 19 18 Maintenance Efficiency 16 14 15 15 Environmental 15 14 14 16  SCORES LEGEND: MAXIMUM REHABILITATION REPLACEMENT OR REHABILITATION MAXIMUM REPLACEMENT  Table 4-7 Results from HOQ for Johnson Bridge - Lyman's Normalization  Residential HOQ Business HOQ  Replacement Rehabilitation Replacement Rehabilitation Economic 18 19 17 14 Social 19 20 21 15 Safety 15 17 16 25 Technical 17 16 16 15 Maintenance Efficiency 15 14 15 16 Environmental 16 14 15 16  SCORES LEGEND: MAXIMUM REHABILITATION REPLACEMENT OR REHABILITATION MAXIMUM REPLACEMENT  Table 4-8 Results from HOQ for Johnson Bridge - Wasserman's Normalization  Residential HOQ Business HOQ  Replacement Rehabilitation Replacement Rehabilitation Economic 24 20 29 22 Social 25 21 30 24 Safety 38 30 46 37 Technical 27 22 32 26 Maintenance Efficiency 32 26 39 31 Environmental 38 31 46 37  SCORES LEGEND: MAXIMUM REHABILITATION REPLACEMENT OR REHABILITATION MAXIMUM REPLACEMENT   96 The three different normalization methods have resulted in three different options for decision with Wasserman's normalization being the most refined among the three. In addition to facilitating a decision between replacement and rehabilitation, the results obtained provide a list of important issues in order of priority that can be used to meet consumer requirements even after the major maintenance is accomplished. For example, environmental issues and safety scored the highest based on Wasserman's normalization. Next on the list were Maintenance Efficiency and Technical. Therefore, even after the bridge is replaced/rehabilitated, adequate measures could be undertaken to address environmental issues and continued maintenance optimization and monitoring. Other factors that ranked low in the HOQ results could also be addressed appropriately when all other factors have been addressed.     97 Chapter  5: Infrastructure User Requirements in QFD using a Hidden Markov Model (HMM)   A version of this chapter has been submitted to the ASCE's Journal of Infrastructure Systems. Bolar, A., Tesfamariam, S., and Sadiq, R. (2014). "Predicting infrastructure user response for quality function deployment (QFD) using hidden Markov model." Journal of Infrastructure Systems (Under review).   5.1 Background 5.1.1 Preliminaries: Markov Chain Basics Definition: Markov chain is a stochastic process with the property that value of a given process 𝑋𝑡 at any time t depends on the value 𝑋𝑡−1 at time t-1 and not on the sequence of other values Xt-2, Xt-3, ……………………………X0 that the process passes through in arriving at 𝑋𝑡−1 . Mathematically, P �Xt �Xt-1,  Xt-2,  Xt-3, ……………………………X0�= P �Xt �Xt-1�    (5-1) Since  𝑋𝑡 depends only on 𝑋𝑡−1 , the process is called a one-step Markov chain. Similarly two-step Markov chain (𝑋𝑡 depends on 𝑋𝑡−1 ,𝑋𝑡−2 ), three-step Markov chain (𝑋𝑡 depends on 𝑋𝑡−1 ,𝑋𝑡−2,𝑋𝑡−3 ) leading to n-step Markov chains (𝑋𝑡 depends on Xt-1 ,Xt-2 ……………………Xt-n) can be defined. States and Transition in Markov Chain: The Markov process as defined above can exhibit a finite number of states depending on the intrinsic nature of the problem. For example, if damage on a structural beam is to be defined in terms of probabilistic states, we can have cracked, corroded, spalled, etc., condition states for the beam. We can call these condition states as state 1, 2, 3 .........m recorded at a given time t. Consider State 1 as ``cracked`` state and State 2 as ``uncracked`` state.   98 Furthermore, let j be the condition state at time t for parameter 𝑋𝑡 and i be the condition state at t-1 represented by parameter 𝑋𝑡−1 . In other words, at a given time t, j or i can have one state among 1, 2, 3..............m. The probability of 𝑋𝑡 being in condition state j given that the condition state was i in  𝑋𝑡−1 is termed as transition probability.    P �Xt=j �Xt-1=i�= Pijt      (5-2) The concept is illustrated in Figure 5-1. Since each i should transit into one of the states represented by j, for any given i, the sum of all transition probabilities should be equal to 1.    ∑ Pijtmj=1 =1   ∀ i       (5-3) Representing the above in a matrix form,   Pij= t-1↓   � t→ 1 2 3 . . m123..m ⎣⎢⎢⎢⎢⎢⎡P11 P12 P13 P1mP21 P22 P23 P2mP31 P32 P33 P3mPm1 Pm2 Pm3 Pmm⎦⎥⎥⎥⎥⎥⎤m x m    (5-4) where, P12, for example, represents the probability of going from condition state 1 at time (t-1) to condition state 2 at time t. The matrix is commonly called as the transition probability matrix (TPM).  For a given condition state i, 𝑃𝑗(0) would represent the probability of being in condition state j at time t=0 as follows,    P(0)= �P1(0) P2(0) . . Pm(0)�1 x m      (5-5) Similarly, for times t = 1, t = n, respectively,    99    P(1)= �P1(1) P2(1) . . Pm(1)�1 x m      (5-6)         P(n)= �P1(n) P2(n) . . Pm(n)�1 x m      (5-7)          Figure 5-1 Markov Chain Transition Possibilities from time (t-1) to (t) If probability 𝑃(0) is known, using the transition probability matrix,    P(1)= �P1(0) P2(0) . . Pm(0)�⎣⎢⎢⎢⎢⎡P11 P12 P13 P1mP21 P22 P23 P2mP31 P32 P33 P3mPm1 Pm2 Pm3 Pmm⎦⎥⎥⎥⎥⎤  (5-8) Probability of going into state 1, P(1) is  P(1) = �P1(0)P11 P2(0)P21 . . Pm(0)Pm1�       (5-9) Therefore, from equations (5-6) & (5-9), t-1 t 1 2 3 . . . m 1 2 3 . . . m Condition State No.   100  �P1(1) P2(1) . . Pm(1)� = �P1(0)P11 P2(0)P21 . . Pm(0)Pm1�    (5-10) or,     P(1) = P(0)Pij        (5-11)    P(2) = P(1)Pij = P(0)Pij x Pij=P0Pij2     (5-12) In general,        P(n) = P(0)Pijn        (5-13) 𝑃(0) is also called as the initial probability matrix and what follows from the above is that given the TPM and initial probabilities, probabilities at any future time step n can be determined by the product of initial probability matrix and the TPM raised to the power n.  5.1.2 Implementing Hidden Markov Model for QFD Hidden Markov Model consists of a stochastic process that is not observable (hidden), but can be observed through an associated stochastic process and thereby generate the sequence of observed symbols (Rabiner & Juang 1986).  Similar implementation of HMM to QFD customer requirements is also provided in Shieh & Wu (2008). The following section provides relevant theory in implementing a HMM methodology.    Continuing from the above summary of Markov model, consider that condition states are represented by a set S = {s1, s2, s3 .......sn} and the observed parameters are represented by set O = {o1, o2, o3......on}. Let {X} be a Markov chain with probability values in state S and J states observed. Let 𝑃𝑗(0) be the absolute probability that sj is in time t0. Therefore   101     P �Xt=j �Xt-1=i�= Pijt     (5-14) The transition probabilities represented by matrix F, is the probability of going from state si to sj is:     F = ⎣⎢⎢⎢⎢⎢⎡Ps1|s1  Ps1|s2  Ps1|s3  Ps1|sm Ps2|s1  Ps2|s2  Ps2|s3  Ps2|sm Ps3|s1  Ps3|s2  Ps3|s3  Ps3|sm Psm|s1  Psm|s2  Psm|s3  Psm|sm ⎦⎥⎥⎥⎥⎥⎤  (5-15)  and the associated observed probabilities i.e. probability that the observed parameter is oj given that the current state is si.     V =Cre ⎣⎢⎢⎢⎢⎢⎡Po1|s1  Po1|s2  Po1|s3  Po1|sml Po2|s1  Po2|s2  Po2|s3  Po2|sm Po3|s1  Po3|s2  Po3|s3  Po3|sm Pol|s1  Pol|s2  Pol|s3  Pol|sm  ⎦⎥⎥⎥⎥⎥⎤  (5-16) where Cre is a credibility factor applied that represents the confidence of the expert estimating the probabilities. Also,      ∑ Psj|si =1mj=1  and  ∑ Pok|j =1mk=1     (5-17) For brevity, represent transition matrix with initial probability as F =  �fj(0)� with state sj and observed probability V =  �Pj(0)� with observed symbols oj associated with state sj.  From the definition of conditional probabilities,  �f1(n) f2(n) . . fm(n)� = �f1(n-1) f2(n-1) . . fm(n-1)�  F for each n ε N   (5-18)   102 �P1(i) P2(i) . . Pl(i)� = ��f1(i) f2(i) . . fl(i)� V for each i ε N U {0} �  (5-19) Considering (5-18) & (5-19)   �P1(n) P2(n) . . Pl(n)� = ��f1(n) f2(n) . . fm(n)� V for each i ε N U {0} �      = �f1(n-1) f2(n-1) . . fm(n-1)�  FV    (5-20) Similar to (5-20), for nth-step,    �P1(n) P2(n) . . Pl(n)� = �f1(0) f2(0) . . fam(0)� FnV   (5-21)  �f1(0) f2(0) . . fm(0)� , matrices F & V can be documented from surveys. If V is square and invertible, using equation 5-19,  �P1(i) P2(i) . . Pl(i)� = ��f1(i) f2(i) . . fl(i)� V for each i ε N U {0} �& �f1(0) f2(0) . . fm(0)�= �P1(0) P2(0) . . Pl(0)�V-1.        �f1(0) f2(0) . . fm(0)�= �P1(0) P2(0) . . Pl(0)�V-1.    (5-22) Therefore,  �P1(n) P2(n) . . Pl(n)� = �P1(0) P2(0) . . Pl(0)�V-1 FnV   (5-23) where 𝑉−1 𝐹𝑛𝑉 is the transformation matrix of observed symbols. Represeting this transformation matrix by TA(n), after 1-step transformation, TA(1) = TA. Equation 5-22 becomes: �Pl(1)� = �P1(0)TA1l+ P2(0)TA2l+P2(0)TA2l+ . . �=∑ Pi(0)TAij for 1≤j≤i l    (5-24) 2-step transformation,   103 �Pl(2)� =∑ Pi(1)TAij i  = ∑ (∑ Pl(0)TAlj)l TAij i =∑ Pl(0)(∑ TAlj)i TAij l       =∑ Pl(0) TAij(2) l =∑ Pl(0) (V-1 F2V) l lj  (5-25) where TAlj2 =(∑ TAlj)i TAij is the 2-step transition-observation transformation matrix. For n-steps,   TAljn =(∑ TAij�n-1�TAlj)i = (V-1 FnV)lj       (5-26) 5.2 Application of QFD HMM to Infrastructure Maintenance 5.2.1 Customer Response Analysis: Case study In order to demonstrate the evaluation of predicting customer response based on the above observed parameters, data was adopted from the California Department of Transportation's 2005 maintenance customer survey available at: http://dot.ca.gov/hq/maint/external_survey/2005_survey/index.htm.  The data available was in the form of pie charts for each question, wherein the questions were regarding maintenance management by the department and responses in linguistic expression.  Therefore, data from the pie charts that were in percentages were mapped into the three categories adopted for the current study, namely High, Medium and Low. Mapping of the data is presented in Table 5-1. The QFD customer requirements (CR) were classified on three scales as follows - High (H) with a weight 5, Medium (M) with a Weight 3 and Low (L) with a weight 1. The scales are also shown graphically in Table 5-2. An Illustrative Example: The solution for HMM for estimating future customer requirements was performed using Microsoft-Excel Visual Basic Application (VBA) programming. However, for demonstration purposes, a solved example is provided for one focus area and 2-steps of future   104 customer requirements. Using the VBA program, any number of future states can be referred to using a drop down box.   5.2.2 Observed Probabilities for Focus Areas Customer requirements in maintenance management are truly dynamic in nature. The reason being that customer requirements certainly vary with time. For example, if customer input is sought for a design and build project, the customer requirements would be valid up to the timeframe during which the project is designed, executed and put into service. Once in service, the customer could exhibit varying levels of expectations and addressing that would be challenging. Furthermore, customer surveys which would form the basis of knowing what is required may have to be repeated when conditions surrounding the intended use of the project change. By using a HMM, some of these challenges can be addressed by adopting the customer requirements as hidden parameters and be predicted using focus areas defined in the study as observed parameters. From maintenance perspective of a civil engineering structure, five key focus areas were proposed as those that would cause greatest impact to customer concerns (Bolar et al. 2014). In the current study, these focus areas are adopted as indicators or observed parameters for predicting customer response. The observed parameters also require a score or value in order to be mathematically used in prediction. Therefore, the observed parameters are assigned a rating value and are explained below:  Economic Factors: The customer response to a survey conducted during good economic condition may be different compared to situations when the economy is weaker. Customer requirements can therefore vary depending on economic conditions and can therefore act as an indicator to predict customer response. In the current study, the economic condition is rated 0 to 1.0 (poor to good).   105 Social Factors: From the point of view of civil infrastructure, changes to social conditions can affect customer perception. For example, influx of population may be good to the social condition of a city, but may add more traffic causing congestion which could have a negative response in a customer survey. Another example could be that opening a new residential sub-division in the city may result in reduced traffic condition. So rather than waiting for the survey to be conducted and for the customer to respond, a change in social condition can aid in predicting customer response. In the current study, social conditions causing poor-to-good situation on a structure is rated on a scale 0-1.  Safety Driven Factors: While one could argue that there is no compromise on safety so there should not be a better or weaker safety condition. However, adopting for example, a new technology can result in a better management of safety related issues. Improvement on safety would definitely be seen by customers as a positive step. Safety driven conditions are rated on a scale 0-1 for poor-to-good safety condition.  Technical Factors: An agency might be able to improve on technical engineering conditions by adopting new technologies, designs, materials and technical expertise. Such expertise could be in the form of personnel, software, etc. Therefore, technical conditions can be seen to improve or worsen with time depending on situations. For example, loss of personnel in an agency can result in reduced technical expertise. In the current study, technical conditions ranging from poor-to-good situation are rated on a scale 0-1. Maintenance Efficiency: Similar to technical factors, adopting new technologies, management systems, materials, etc can result in improved maintenance. In the current study, maintenance efficiency is rated 0-1 ranging from worse to improved condition.   106  Environmental Factors: With customers becoming more conscious over issues involving sustainability, environmental factors surrounding a maintenance decision can be of great concern to the customer. Improved environmental conditions can hold satisfactory value to the customer, whereas degrading environmental conditions may be unsatisfactory. Therefore, predicted environmental factors can correlate positively with customer responses in a survey. In the current study, predicted environmental factors are rated 0-1 ranging from worse to improved condition. The rating system explained for each of the above observed parameters requires expert input in order to be assigned. Few parameters, economic condition for example, may already have predictions by various experts and even on a daily basis. Social factors could be extrapolated from government agencies dealing with such issues. Safety Driven, Technical Factors, Maintenance Efficiency and Environmental Factors could be rated by the management authority of the agency seeking customer input. Since there can be variation in the rating depending on the confidence of the expert assigning the rating value, a credibility factor is applied to the ratings obtained. For the current study, the rating is obtained based on expert judgment of the author. The ratings, credibility factors and reasoning have been provided in Table 5-3  Having established the QFD customer requirements scale, transition probabilities, and emission probabilities in Table 5-3, all these parameters can be input into equations 14-25 for estimating future probabilities of customer requirements.  The CRs can then be used in QFD for prioritization of HOWs using QFD relationship and correlation matrices. The QFD relationship matrix and correlation matrix in Figure 5-2 were obtained from expert judgment of the author using a 5 tier scale between 1 & 9, where 1 represents weak relationship and 9 represents strong relationship. For example, most of the questions in Table 5-1 are related to customer satisfaction and therefore a rating '9' has been assigned to the HOW "customer satisfaction." Question No. 3 in Table 5-1 is   107 related to removing graffiti from areas and the use of "Toll" for removing graffiti would be a very unlikely situation and therefore a relationship rating of "one" has been assigned in this case. Starting with the economic condition probabilities in Table 5-3  𝐶𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 𝑆𝑡𝑎𝑡𝑒𝑠, 𝑆 = � 5 3 1 � 𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑀𝑎𝑡𝑟𝑖𝑥,𝐹𝑖𝑗 = �0.5 0.4 0.10.3 0.6 0.10.3 0.6 0.1� 𝐸𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑀𝑎𝑡𝑟𝑖𝑥,𝑉 = �0.6 0.4 00.7 0.3 00.3 0.6 0.1� 𝑉−1 = �−3 4 07 −6 0−33 24 10� 𝑉−1𝐹1 = �−0.3 1.2 0.11.7 −0.8 0.1−6.3 7.2 0.1� (Note that n=1 for step 1, therefore 𝑃𝑛 = 𝑃) 𝑉−1𝐹𝑉 = �0.69 0.30 0.010.49 0.5 0.011.29 −0.3 0.01� 𝐹1𝑗𝑉−1𝐹𝑛𝑉 = {0.84 0.07 0.09} �0.69 0.30 0.010.49 0.5 0.011.29 −0.3 0.01�  =  {0.73 0.26 0.01}  𝑆𝐹1𝑗𝑉−1𝐹𝑛𝑉 = {0.73 0.26 0.01} � 5 3 1 �  = 4.44    108 Table 5-1 Mapping of CALTRANS Linguistic Data to Numerical Rating System CALTRANS Question7Answer Choices 7  Response Percentage7 Rating Initial Probability for HMM 1 How long do you feel it should take to repair/replace safety barriers, guard rails, and median barriers? Same day 19% High 82% Up to two days 33% Two days to a week 30% Two weeks 2% Medium 4% Two to four weeks 2% Depends on other priorities 7% Low 9% No Opinion 2% 2 How long should it take Caltrans to repair signs (excluding Stop and Yield signs) after they have been damaged? Same day 25% High 86% Up to two days 32% Two days to a week 28% Two weeks 7% Medium 9% Two to four weeks 2% Depends on other priorities 5% Low 6% No Opinion 1% 3 How long should it take Caltrans to remove graffiti from areas other than signs? Same day 8% High 53% Up to two days 16% Two days to a week 29% Two weeks 15% Medium 23% Two to four weeks 8% Depends on other priorities 21% Low 24% No Opinion 3% 4 How would you grade the job Caltrans is doing repairing potholes on the highway you drive most often? Excellent 11% High 46% Good 35% Fair 32% Medium 32% Poor 21% Low 22% No Opinion 1% 5 What is the biggest concern you have regarding California's bridges and overpasses? Structural Safety 40% High 40% Traffic Congestion 33% Medium 33% Poor riding pavement 13% Low 27% Other 14%                                                  7  http://dot.ca.gov/hq/maint/external_survey/2005_survey/SurveyResults/StatewideResults.pdf   109 Table 5-2 Customer Requirement States  STRONG    WEAK Value 5  3  1 Relationship HIGH  MEDIUM  LOW  Therefore, the weight of customer requirement in the future after 1-step is evaluated as 4.44.  For step two, the transition probability matrix has to be raised to the power 2, therefore, 𝑃𝑛 = 𝑃2 = 𝑃𝑥𝑃  𝑉−1𝐹2 = 𝑉−1𝐹𝐹 = �0.24 0.66 0.10.64 0.26 0.1−0.96 1.86 0.1� 𝑉−1𝐹2 = 𝑉−1𝐹𝐹𝑉 = �0.64 0.35 0.010.60 0.39 0.010.76 0.23 0.01� 𝐹1𝑗𝑉−1𝐹𝑛𝑉 =  {0.84 0.07 0.09} �0.64 0.35 0.010.60 0.39 0.010.76 0.23 0.01� = {0.64 0.35 0.01} 𝑆𝐹1𝑗𝑉−1𝐹𝑛𝑉 =  {0.64 0.35 0.01} � 5 3 1 �  = 4.27  Therefore, after two time steps, the customer requirement in future is evaluated to be 4.27. Similarly, the customer requirement is calculated from each of the focus areas and are presented in Table 5-4.   110 Table 5-3 Expert Opinion on Transition/Emission Probabilities  Credibility Factors  Transition Probabilities Emission Probabilities Summary Weak Average Strong Weak Average Strong  Economic 0.8 Weak 0.50 0.40 0.10 0.60 0.40 0.00  Transitions probabilities are assigned for each of the categories transiting from Weak-to- Strong/Average/Weak, Average-to- Strong/Average/Weak, Weak-to-Strong/Average/Weak. For each of the Categories, credibility factors have been assigned based on the confidence with which the expert could have assigned the probabilities. For example, the economic expert may have a 80% confidence in judging the transitions, whereas an expert on social issues many have only 70% confidence in the social conditions predicted.  Average 0.30 0.60 0.10 0.70 0.30 0.00 Strong 0.30 0.60 0.10 0.30 0.60 0.10 Social 0.7 Weak 0.60 0.40 0.00 0.70 0.30 0.00 Average 0.30 0.60 0.10 0.20 0.60 0.20 Strong 0.00 0.20 0.80 0.00 0.40 0.60 Safety 0.65 Weak 0.60 0.40 0.00 0.70 0.30 0.00 Average 0.30 0.60 0.10 0.20 0.60 0.20 Strong 0.00 0.20 0.80 0.00 0.40 0.60 Technical 0.75 Weak 0.60 0.40 0.00 0.70 0.30 0.00 Average 0.30 0.60 0.10 0.20 0.60 0.20 Strong 0.00 0.20 0.80 0.00 0.40 0.60 Maintenance  Efficiency 0.9 Weak 0.60 0.40 0.00 0.70 0.30 0.00 Average 0.30 0.60 0.10 0.20 0.60 0.20 Strong 0.00 0.20 0.80 0.00 0.40 0.60 Environmental 0.85 Weak 0.60 0.40 0.00 0.70 0.30 0.00 Average 0.30 0.60 0.10 0.20 0.60 0.20 Strong 0.00 0.20 0.80 0.00 0.40 0.60   111 5.2.3 Discussion  Predicting the customer's opinion from a cognitive point of view may be a complex process and outside the scope of this research. However, starting with available customer responses as input, the focus areas of attention for the customer (economic, social, technical, maintenance efficiency and environmental issues) were adopted for estimating future customer requirements. These estimated customer requirements present a best estimate of expectations of the customer in the absence of actual surveys. In the above worked example, existing customer requirements were systematically used in a 1-step HMM followed by two steps, in order to demonstrate how future customer requirements at two time steps can be evaluated. The customer requirements from 2-step hidden Markov analysis are provided in Table 5-4. Using a simple VBA macro, the same calculation methodology has been extended to any number of time steps possible. Furthermore, the remaining focus areas can also be included and future customer requirements can be determined. These future requirements can be used, for example, in prioritization, for identifying at what future state, which QFD HOW (action for satisfying customer requirement) would be of importance. Using the prioritization scheme in Bolar et al. (2013), the future customer requirements are input to QFD House of Quality for updating prioritizations evaluated. Figure 5-2 shows the HOQ with CRs evaluated using the HMM.     112  Table 5-4 Summary of Customer Requirements from 2-Step Hidden Markov Analysis Economic Social Safety Technical Maintenance  Environmental COMBINED 4.27 2.59 3.28 3.28 3.28 3.28 3.33 4.22 4.22 4.22 4.22 4.22 4.22 4.22 3.86 3.86 3.86 3.86 3.86 3.86 3.86 3.36 3.36 3.42 3.36 3.36 3.49 3.39 3.09 3.09 3.09 5.31 3.42 3.09 3.51    113  Figure 5-2 Customer Requirement (Relative Importance) Obtained using Hidden Markov Analysis  114 Chapter  6: Conclusions and Recommendations 6.1 Summary Proposed QFD-based infrastructure management framework  has an ability to facilitate improved decision-making through following: • customer voice related to infrastructure is systematically incorporated in the decision framework • condition assessment is improved by the use of interval ratings and by incorporating and propagating uncertainty • future customer requirements are evaluated using expert judgement for use within the QFD process Decision-making in existing Bridge Management Systems (BMSs) do not incorporate customer voice directly and is based on quantitative data with limited expert input (such as in generating transition probabilities for element deterioration in Pontis). The framework proposed in this thesis can be adopted either for quantitative data or expert-based information. Current bridge management practices are mostly based on human judgment and incorporating a voice from the end user of the infrastructure would add considerable value to the decision-making process. Furthermore, the use of condition assessment techniques based on HER framework facilitates improved handling of uncertainty. Overall, these improvements provide the decision-maker an effective tool to evaluate, control and mitigate risk effectively.    115 6.2 Specific Contributions - Chapter 3  Current condition rating of bridges reflects either an aggregate (overall) state of its health such as an NBI rating evaluation, or evaluation of individual elements. Either of these methods represents two extremes in evaluating structural condition. The condition assessment can be made more effective by determining condition of groups of elements classified based on their resilience. Furthermore, current Bridge Management Systems (BMS) are customized to suit every Bridge agency's inventory. A common classification scheme for condition rating would serve as a benchmark for identifying relatively higher distress and allocation of resources for necessary action. As an example, for prioritizing risk among an inventory of bridges in a given city,  instead of comparing either overall rating or maybe individual primary element ratings (such as deck rating), primary indices as evaluated in this study could be compared and the higher distressed indices among them could be prioritized for further investigation. Comparison between overall bridge ratings would not reflect state of individual primary elements and comparing each such single primary component (such as deck, superstructure) for an inventory of bridges could prove tedious. The present model is built on a hierarchical framework for bridge condition assessment in which all contributory factors (or attributes) are assumed independent, and only the parallel aggregation of factors (or attributes) are performed using DS rule of combination. The proposed model presented in this study is still in its infancy, and extensive work needs to be done to classify bridge elements and make algorithm HER more robust to deal with dependent factors as well as to effectively deal with the issue of “conflict” using alternative rules of combination.     116 6.3 Specfic Contributions - Chapter 4  Quality Function Deployment (QFD) has been illustrated for use in maintenance of infrastructure using bridges as an example. The maintenance applications demonstrated in this study include inspection prioritization and decision-making scenarios for replacement or rehabilitation. In both cases, three different normalization methods were used to demonstrate the impact of the methods in QFD processes. Appropriate ranking of inspection items were generated for use in existing inspection items and schedules. The decision-making scenarios generated distinct results for each of the normalization cases that could aid major decision-making. Implementing a QFD process as is done in the manufacturing industry has involvement from various disciplines ranging from design to the final production process. For a bascule type bridge adopted in the case study, the concerns may not be just structural, but also involve other disciplines such as mechanical, electrical, etc. The involvement of such personnel may open the door to discussion and generate unimaginable HOWs that are relevant in addition to improving quality of maintenance. HOWs could be generated by each of the disciplines individually and then combined in various ways such as based on priority items for each disciplines, etc. Using the correlation matrix, duplication of effort can be eliminated by examining strongly correlated HOWs, research on trade-off items identified by negatively correlated HOWs may lead to innovation and cost-reduction. Looking at the relationship matrix, the zeroes could quickly identify that the proposed HOW may not work for the given WHAT thereby identifying flaws and issues early in the process. In addition to all the benefits, the most important objective fulfilled by implementing QFD would be increased customer satisfaction which for the case of infrastructure would be citizens and thereby lead to improved societal conditions.     117 6.4 Specific Contributions - Chapter 5 A Hidden Markov Model (HMM) has been employed for dealing with dynamic customer requirements in an application involving infrastructure maintenance. Customer involvement can be minimal in civil engineering applications leading up to design stages. However, in engineering maintenance, customer requirements can be considered truly dynamic - as time proceeds, maintenance needs of a structure change and so does customer requirements. Capturing customer requirements constantly may be difficult as conducting surveys, collecting information, synthesis, and generating outcomes involve time, human efforts and cost. Using a hidden Markov model, expert opinion can be sought from individuals, government agencies or departments with regards to focus areas for the customer. Using those expert probabilities for the focus area as hidden Markov parameters, estimation of future customer requirements have been circumvented thereby eliminating the need for repeated customer surveys.  6.5 Limitations of this Research The QFD-based framework presented in this thesis relies mostly on customer and expert input and can therefore be subjective leading to epistemic uncertainty. While the condition assessment uncertainty is addressed by the use of HER framework, the QFD process in the framework does not include any algorithms or techniques for addressing uncertainty arising from sources such as customer input, expert input in the relationship matrix, etc. Also, there is no deterioration model for the interval-based condition assessment in order to predict deteriorated condition of elements. The ability to predict deteriorated condition would facilitate further scenarios such as cost-benefit analysis. For the HMM implementation, the estimated probabilities are assumed to be free of uncertainties and focus areas adopted for the study that were based on sustainability issues only. In addition, while case studies have been presented for demonstrating applications,   118 further validation of the methodology would prove valuable. For example, in HMM implementation, successive surveys could be performed at a few time intervals and the results could aid in calibrating the probabilities proposed by experts in each of the focus areas. Lastly, the framework comprises of only a portion of an entire life-cycle management framework. 6.6 Recommendations All the improvements proposed in this thesis can be practically implemented for decision-making as demonstrated by the use of case studies. However, acceptance of the approach by an infrastructure or bridge maintenance agency would further validate the procedure and improve bridge maintenance coupled with customer satisfaction. The evidential reasoning techniques that were adopted for condition assessment within the framework should be extended to QFD and HMM sections of the framework thereby addressing both epistemic and aleatory uncertainties. A similar evidence theory-based deterioration model for condition assessment should be incorporated leading to the use of cost-benefit scenarios. Alternatively, a QFD-based life cycle assessment framework could be developed that incorporates additional relevant stages such as material procurement, disposal, recycling, etc. The extension of the framework by adding such options could lead to challenges in computation and database management that should be explored for efficient operation of the process. 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The frame of discernment in this case would be: Θ = {CS-1, CS-2, CS-3, CS-4, CS-5} and the number of subsets is 2Θ = 25 = 32 and are: [Φ, {CS-1}, {CS-2}, {CS-3}, {CS-4}, {CS-5},{CS-1, CS-2}, {CS-1, CS-3}, {CS-1, CS-4}, {CS-1, CS-5}, {CS-2, CS-3}, {CS-2, CS-4}, {CS-2, CS-5}, {CS-3, CS-4},{CS-3, CS-5}, {CS-4, CS-5}, {CS-1, CS-2, CS-3} ,{CS-1, CS-2, CS-4}, {CS-1, CS-2,CS-5}, {CS-1, CS-3, CS-4}, {CS-1, CS-3, CS-5}, {CS-1, CS-4, CS-5}, {CS-2, CS-3, CS-4}, {CS-2, CS-3, CS-5}, {CS-2, CS-4, CS-5}, {CS-3, CS-4, CS-5}, {CS-1, CS-2, CS-3, CS-4}, {CS-1, CS-2, CS-3, CS-5}, {CS-1, CS-2, CS-4, CS-5},{CS-1, CS-3, CS-4, CS-5},{CS-2, CS-3, CS-4, CS-5}, Θ].  The basic probability assignment (BPA), an important concept in DST, reflects a degree of belief in a hypothesis or the degree to which the evidence supports the hypothesis. BPA has the following properties, 1)( =∑ ΨΘ⊆Ψm ; 0)( =φm ; ,1)(0 ≤Ψ≤ m  for all Θ⊆Ψ      (A-1) where )(Ψm  represents the direct support of evidence on Ψ, i.e., indicates that portion of the total belief exactly committed to hypothesis Ψ given a body of evidence. BPA, with interval   135 value of [0, 1], can be assigned to every subset Ψ (where Ψ ⊆ Θ). If the existing evidence cannot differentiate between two hypotheses, say, Ci and Cj, a BPA could be assigned to the subset that consists both of these hypotheses, denoted by m({Ci , Cj}). The quantity m(Θ) is a measure of that portion of the total belief that remains unassigned after commitment of belief to all subsets of Θ. If m(Ψ) = s, and no BPA is assigned to other subsets of Θ, then m(Θ) = 1 - s. Thus, the remaining BPA is assigned to Θ itself, but not to the negation of a subset Ψ. This value of BPA m(Θ) represents ignorance. Example 2: Consider Θ = {CS-1, CS-2, CS-3, CS-4, CS-5}, denoted as H = {H1, H2, H3, H4, H5} that represents five condition states as determined by investigation. Assume that the information obtained indicates that m({H1}) = 0.25, m({H2}) = 0.10, m({H3}) = 0.40, ({H4}) = 0.05, ({H5}) = 0.10, i.e., the degree to which the evidence supports these condition states is 25%, 10%, 40%, 5% and 10%, respectively. Hence, BPA assigned to ignorance is m(Θ) = 1 - (0.25 + 0.10  + 0.40 + 0.05 + 0.10) = 0.10. It can then be interpreted that the set of all conditions states {H1, H2, H3, H4, H5} possess 10% unassigned mass (probability) based on available incomplete evidence.  A.2 Combining Two Bodies of Evidence using Dempster Rule  Example 3: Consider two elements of a steel bridge superstructure. The condition of truss girder (element 1) is reported as m({CS-4}) = 60% and m({CS-3, CS-4}) = 15% which means that the condition state is CS-4 with a 60% confidence and will be either CS-3 or CS-4 with a 15% confidence.  Similarly, the condition of the horizontal bracing (element 2) is reported as m({CS-1}) = 70% and m({CS-1, CS-2} = 10%. The data (bodies of evidence) of the two elements are to be combined to get a measure of the superstructure condition. Both elements are assumed to have   136 five condition states and continuing from Example 2, Figure A-1 provides the subsets for girder condition and bracing condition in a matrix form. If the intersection of the two bodies of evidence would produce an empty set, the symbol Φ is shown (i.e., A ∩ B = Φ). For cases where the intersection would not produce a null set, the symbol ∩ is used. Ignorance evaluated is represented by the symbol ∩ in bold letters. Using, Φ≠Ψ−∑Φ=Ψ=Ψ⊕Ψ=ΨΘ⊆∀Ψ=∩ when1)()(when0)()()(,,212112KBmAmmmmBABA      (A-2) for combining the two sets of data, A ∩ B = Ψ is required. K is represented by combination of all bodies of evidence where the set intersection produces a null set, i.e., adding up all data represented by Φ in the Figure A-1 matrix. Therefore: {A ∩ B}Φ = Φ = K = {(0.7 x 0.60) + (0.7 x 0.15) + (0.1 x 0.6) +(0.1 x 0.15)} = 0.60 {A ∩ B}1 = Ψ1 / (1-K) = {CS-1} = {(0.7 x 0.25) / (1-0.6) } = 43.75% {A ∩ B}2 = Ψ2 / (1-K) = {CS-1, CS-2} = {(0.1 x 0.25) / (1-0.6)} = 6.25% {A ∩ B}3 = Ψ3 / (1-K) = {CS-4} = {(0.2 x 0.6) / (1-0.6)} = 30% {A ∩ B}4 = Ψ4 / (1-K) = {CS-3, CS-4} = {(0.2 x 0.15) / (1-0.6)} = 7.5% Based on the above combination, the superstructure condition can be rated as 43.75% CS-1 and 30% CS-4.   137  Figure A-1 An Example of Combining Two Bodies of Evidence Obtained from Bridge Inspection{CS-1}{CS-2}{CS-3}{CS-4}{CS-5}{CS-1, CS-2}{CS-1, CS-3}{CS-1, CS-4}{CS-1, CS-5}{CS-2, CS-3}{CS-2, CS-4}{CS-2, CS-5}{CS-3, CS-4}{CS-3, CS-5}{CS-4, CS-5}{CS-1, CS-2, CS-3}{CS-1, CS-2, CS-4}{CS-1, CS-2,CS-5}{CS-1, CS-3, CS-4}{CS-1, CS-3, CS-5}{CS-1, CS-4, CS-5}{CS-2, CS-3, CS-4}{CS-2, CS-3, CS-5}{CS-2, CS-4, CS-5}{CS-3, CS-4, CS-5}{CS-1, CS-2, CS-3, CS-4} {CS-1, CS-2, CS-3, CS-5} {CS-1, CS-2, CS-4, CS-5}{CS-1, CS-3, CS-4, CS-5}{CS-2, CS-3, CS-4, CS-5}{CS-1, CS-2, CS-3, CS-4, CS-5}0.6000.1500.250{CS-1 } 0.700 ∩ ∅ ∅ ∅ ∅ ∩ ∩ ∩ ∩ ∅ ∅ ∅ ∅ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∅ ∅ ∅ ∩ ∩ ∩ ∩ ∅ ∩{CS-2 } ∅ ∩ ∅ ∅ ∅ ∩ ∅ ∅ ∅ ∩ ∩ ∩ ∅ ∅ ∅ ∩ ∩ ∩ ∅ ∅ ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∅ ∩ ∩{CS-3 } ∅ ∅ ∩ ∅ ∅ ∅ ∩ ∅ ∅ ∩ ∅ ∅ ∩ ∩ ∅ ∩ ∅ ∅ ∩ ∩ ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩{CS-4 } ∅ ∅ ∅ ∩ ∅ ∅ ∅ ∩ ∅ ∅ ∩ ∅ ∩ ∅ ∩ ∅ ∩ ∅ ∩ ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩{CS-5 } ∅ ∅ ∅ ∅ ∩ ∅ ∅ ∅ ∩ ∅ ∅ ∩ ∅ ∩ ∩ ∅ ∅ ∩ ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩{CS-1, CS-2 } 0.100 ∩ ∩ ∅ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-3 } ∩ ∅ ∩ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-4 } ∩ ∅ ∅ ∩ ∅ ∩ ∩ ∩ ∩ ∅ ∩ ∅ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-5 } ∩ ∅ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∅ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-2, CS-3 } ∅ ∩ ∩ ∅ ∅ ∩ ∩ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-2, CS-4 } ∅ ∩ ∅ ∩ ∅ ∩ ∅ ∩ ∅ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-2, CS-5 } ∅ ∩ ∅ ∅ ∩ ∩ ∅ ∅ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-3, CS-4 } ∅ ∅ ∩ ∩ ∅ ∅ ∩ ∩ ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-3, CS-5 } ∅ ∅ ∩ ∅ ∩ ∅ ∩ ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-4, CS-5 } ∅ ∅ ∅ ∩ ∩ ∅ ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-2, CS-3 } ∩ ∩ ∩ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-2, CS-4 } ∩ ∩ ∅ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-2,CS-5 } ∩ ∩ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-3, CS-4 } ∩ ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-3, CS-5 } ∩ ∅ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-4, CS-5 } ∩ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-2, CS-3, CS-4 } ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-2, CS-3, CS-5 } ∅ ∩ ∩ ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-2, CS-4, CS-5 } ∅ ∩ ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-3, CS-4, CS-5 } ∅ ∅ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-2, CS-3, CS-4 } ∩ ∩ ∩ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-2, CS-3, CS-5 } ∩ ∩ ∩ ∅ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-2, CS-4, CS-5 } ∩ ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-3, CS-4, CS-5 } ∩ ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-2, CS-3, CS-4, CS-5 } ∅ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩{CS-1, CS-2, CS-3, CS-4, CS-5 } 0.200 ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩GIRDER CONDITIONHORIZONTAL BRACING CONDITION  138 Appendix B  : Management of Civil Infrastructure Systems - a QFD-Based Approach B.1 Frame of Discernment & Ignorance Computation Examples These methods involve two operative steps (Akao, 1988). The first step is the conversion of the relationships between customer requirements (‘whats’) and product or technical characteristics (‘hows’) from symbols (e.g., “∆”, “ο” and “ ⋅ ” for weak, medium and strong relationships, respectively) to equivalent numbers. Different scales are used for this transformation, but the standard system of weights 1 (weak), 3 (medium), 9 (strong) more commonly used (Franceschini, 2002) is chosen in this study. The second step allows computation of the level of importance, wj of each ‘how’. The relative importance of each ‘what’ is multiplied by the quantitative value of the relationship existing between that j-th ‘how’ and each of the ‘whats’ related to it. Therefore, the results are summarized (Franceschini, 2002) as follows: 1nj i ijiw d r== ⋅∑             (B-1) where wj is the technical importance rating of the j-th product characteristic (e.g., use green materials and construction methods), id  is the degree of relative importance of the i-th customer requirement (e.g., environmentally safe maintenance), ijr  is the cardinal relationship between the i-th customer requirement and the j-th product characteristic, i = 1, 2, ..., n; j = 1, 2, ..., m; n is the number of ‘whats’ and m is the number of ‘hows’. Differences between the three methods are in the expression of ijr , as described below: • Independent scoring method: ijr  is, in this study, the correlation between the i-th ‘what’ and the j-th ‘how’; • Lyman’s normalization method: the coefficients rij in the relationship matrix are normalized by dividing the value of each coefficient rij by the sum of the rij values of each row. The normalized coefficient ijr is of this form: 1ijij mijjrrr==∑            (B-2) • Wasserman’s normalization method: the coefficients rij in the relationship matrix are normalized, taking into account the interdependency between the product characteristics (the roof of the HoQ, described earlier). The expression of the normalized coefficient ,normi jr  is as follows:   139 ( )( ), ,1,, ,1 1mi k k jnorm ki j m mi j j kj krrr== =⋅ γ=⋅ γ∑∑∑          (B-3) where jkγ  is the intensity of the correlation between product characteristic j (e.g., increased taxes) and product characteristic k (e.g., Enhanced overlay quality).  In the Lyman’s normalization, the correlations between the ‘hows’ (the correlation matrix), constituting the roof of the HoQ are not considered. Yet, these correlations may play an important role in prioritizing ‘hows’. Wasserman (1993) proposes an extension of the Lyman’s normalization. In this method, the dependency is modeled by determining the vector space of ‘hows’ and that of customer requirements. Franceschini (2002) illustrated the process, as follows: • If { }iu(i = 1, 2, …, n) are the unit vectors that generate the vector space Φ  of customer requirements or needs (Good condition of road surface, improved visibility of traffic signs, etc), and if we consider the customer requirements or needs are independent one another (not correlated), the set of vectors { }iu forms an orthogonal basis spanning the customer requirements space Φ . Then, the vector dof customer importance rating is of this form: 1 21 2. . ... .n nd d u d u d u= + + +            (B-4) where di (i =1, 2, …, n) is the importance of the i-th customer requirement. • If { }jv (j = 1, 2, …, m) are the unit vectors that generate the vector space Ω of ‘hows’ (the set of vectors { }jv does not necessarily form an orthogonal basis, as it may have linear dependency between the ‘hows’), the intensity jkγ of correlation between product characteristic j (e.g., increased taxes) and product characteristic k (e.g., enhanced overlay quality) is of the form: v v ( cos(v , v ))jk j jk kγ ≡ ⋅ ≡            (B-5) The values of jkγ  must be between 0 and 1. Then if the scale (1, 3, 9) was used for the correlations (weak, medium, strong) between customer requirements and product characteristics, the values 0.1 (weak), 0.3 (medium) and 0.9 (strong) can be assigned to jkγ .   140 As 1 1 1 1n n n mi j iji j i jv v= = = =    ⋅ = γ          ∑ ∑ ∑∑ , a generalization of Lyman’s normalization referred to correlated product characteristics is expressed by Eq. (B-6) below, and is satisfied by calculating the normalized coefficients using Eq. (B-3) above.  ( ) ( )1 2 1 2,1 ,2 ,... ... 1norm norm norm n ni i i nr v r v r v v v v⋅ + ⋅ + + ⋅ ⋅ + + + =           (B-6) where i =1, 2, …, n. To facilitate the understanding, let us consider a hypothetical example. Customers have two requirements or needs (‘whats’) – ‘Improved Surface Conditions’ with relative importance of 20%, and ‘Enhanced Aesthetics of Bridge’ with relative importance of 80%.  Let us consider two types of product or technical characteristics (‘hows’) that help to meet these two customer requirements. The product characteristics_ type 1 (PC_T1) contains following four ‘hows’: Deck Overlay, Approach Slab Overlay, Alkali-Silica Reaction (ASR), Expansion Joints. The relationship is strong between each one of these sub-characteristics and the customer requirement ‘Improved Surface Conditions’ for a bridge. The product characteristics type 2 (PC_T2) is constituted of eight sub-characteristics: Paint on Steel, Concrete Coatings, Handrails, Sidewalk, Wingwalls, Culvert, Deck, Flags/Signs. Each of them is strongly correlated with the ‘what’ Enhanced Aesthetics of Bridge'.  Table B-1 presents the results of prioritizing product characteristics using the independent scoring method. The product characteristics PC_T1 connected only to the customer requirement ‘Improved Surface Conditions’ obtain a weight of 66.67%, whereas the weight of product characteristics PC_T2, in relation with customer requirement ‘Enhanced Aesthetics of Bridge', is 33.33%. These values are computed using Eq. (B-1), as follows: 4 4 2_ 11 1 112 12 2_ 25 5 1_ 1(20 0 80 9) (20 0 80 9) (20 0 80 9) (20 0 80 9) 2880(20 9 80 0) (20 9 80 0) (20 9 80 0) ... (20 9 80 0) 1440(%) (2880 / (2880 1440PC T j i ijj j iPC T j i ijj j iPC Tw w d rw w d rw= = == = == = ⋅ = × + × + × + × + × + × + × + × == = ⋅ = × + × + × + × + × + × + + × + × == +∑ ∑∑∑ ∑∑_ 2)) 100 66.67(%) (1440 / (2880 1440)) 100 33.33PC Tw × == + × = The contribution of customer requirements ‘Improved Surface Conditions’ and ‘Enhanced Aesthetics of Bridge’ to overall satisfaction of customer is in a proportion of 1/4 (20% for ‘Improved Surface Conditions’ divided by 80% for ‘Enhanced Aesthetics of Bridge’). It was expected a similar proportion between the levels   141 of relative importance of PC_T2 and PC_T1. According to results (Table B-1) this proportion is 1/2, because PC_T2 is expressed by a greater number of sub-characteristics (i.e., 8) than PC_T1 (i.e., 4). Therefore its relative importance was artificially ballooned (Franceschini, 2002) from 20% to 33.33%.  To solve this problem Lyman (1990) proposes to normalize the coefficients rij [Eq. (B-2)]. Table B-2 shows the results of the Lyman’s normalization method. The proportion between the levels of relative importance of PC_T2 and PC_T1 is reduced to 1/4, as expected. Results of Table B-2 are calculated as follows: 4 4 2 4 2_ 1 121 1 1 1 1112 12 2 12 2_ 2 125 5 1 5 110 9 0 9 0 9 0 9(20 80 ) (20 80 ) (20 80 ) (20 80 )72 36 72 36 72 36 72 369 0(20 8072 380ijijPC T j i ij j i j iijjijijPC T j i ij j i j iijjrw w d r drrw w d r dr= = = = === = = = ==× + × + × + × + × + × + × + ×× + ×= = ⋅ = ⋅ = == = ⋅ = ⋅ =∑ ∑∑ ∑∑∑∑ ∑∑ ∑∑∑_ 1_ 29 0 9 0 9 0) (20 80 ) (20 80 ) ... (20 80 )6 72 36 72 36 72 3620(%) (80 /100) 100 80(%) (20 /100) 100 20PC TPC Tww+ × + × + × + × + + × + × = = × = = × = However, Wasserman (1993) proposes an extension of the Lyman’s method. Although the latter allows obtaining the expected proportion between the levels of relative importance of the two types of product characteristics, it does not consider the possible interactions among these characteristics. The Wasserman’s method provides a more realistic way to determine the relative importance of each product characteristic. In addition, this method also allows the use of one product characteristic if i) this product characteristic is strongly correlated with another product characteristic (i.e., together they provide redundant information) and ii) these two product characteristics have equal impacts on the customer requirement(s). Introducing/improving only one of these two (or more) product characteristics allows meeting the same level of the customer satisfaction (that would allow improving these two or more correlated product characteristics) and reduces the monitoring and management costs.  For demonstration purpose, let us consider that there are correlations among some product characteristics. Table B-4 presents these fictitious correlations (e.g., strong correlation between approach slab overlay and Alkali-Silica Reaction - ASR). Using Eq. (B-3), normalized coefficients ,normi jr  between each product characteristic and each customer requirement are computed (Table B-3). For example, the Wasserman’s normalized correlations 1,1normr  and 2,1normr (between ‘improved surface condition’ (a ‘what’) and deck overlay (a ‘how’) and between ‘enhanced aesthetics of bridge’ (a ‘what’) and deck overlay, respectively), are computed as follows:    142 1,1 1,1 1,2 2,1 1,3 3,1 1,12 12,11,11,1 1,1 1,2 1,12 1,2 2,1 2,2 2,12 1,12 12,1 12,2 12,121,10 1 0 0.3 0 0.9 0 0.3 9 0 9 0 9 0 9 0 9 0 9 0 9 0 9...( ... ) ( ... ) ... ( ... )normnormr r r rrr r rr× + × + × + × + × + × + × + × + × + × + × + ×⋅ γ + ⋅ γ + ⋅ γ + + ⋅ γ=γ + γ + + γ + γ + γ + + γ + + γ + γ + + γ=00 (2.5) 0 (2.2) 0 (1.9) 0 (2.2) 9 (1.0) 9 (1.0) 9 (1.0) 9 (1.0) 9 (1.0) 9 (1.9) 9 (1.9) 9 (1.9)0× + × + × + × + × + × + × + × + × + × + × + ×=and  2,1 1,1 2,2 2,1 2,3 3,1 2,12 12,12,12,1 1,1 1,2 1,12 2,2 2,1 2,2 2,12 12,12 12,1 12,2 12,122,19 1 9 0.3 9 0.9 9 0.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0...( ... ) ( ... ) ... ( ... )normnormr r r rrr r rr× + × + × + × + × + × + × + × + × + × + × +⋅ γ + ⋅ γ + ⋅ γ + + ⋅ γ=γ + γ + + γ + γ + γ + + γ + + γ + γ + + γ=09 (2.5) 9 (2.2) 9 (1.9) 9 (2.2) 0 (1.0) 0 (1.0) 0 (1.0) 0 (1.0) 0 (1.0) 0 (1.9) 0 (1.9) 0 (1.9)0.284×× + × + × + × + × + × + × + × + × + × + × + ×= The weight of deck overlay is computed using Eq. (B-3) as follows: 2,120 0 80 0.284 23normj i i jiw d r== ⋅ = × + × =∑     j = 1 (deck overlay) The process is identical for the other 11 product characteristics. The expected proportion (1/4) between the levels of relative importance of the two types of ‘hows’, i.e., PC_T2 and PC_T1, is also obtained using this normalization method (Table B-1).  Obviously, the example above is hypothetical and exaggerated for improving the understanding in the mathematical aspects of the proposed approach in the paper.   143 Table B-1 Prioritizing product characteristics using Independent Scoring Method: an exaggerated example  Product Characteristics (or technical characteristics or design requirements) (HOWs)   Product Characteristics Type 1 Product Characteristics Type 2 Customer Requirements (WHATS) Weights of  WHATs (di) Deck Overlay Approach Slab Overlay Alkali Silica Reaction (ASR) Expansion Joints Paint on Steel Concrete Coatings Handrails Sidewalk Wingwalls Culvert Deck Flags/Signs Improved Surface Conditions 20.00% 0 0 0 0 9 9 9 9 9 9 9 9 Enhanced Aesthetics of Bridge 80.00% 9 9 9 9 0 0 0 0 0 0 0 0 Individual Weight (wj) 720 720 720 720 180 180 180 180 180 180 180 180 Total weights of HOWs (absolute importance) 2880 1440 Total weights of HOWs (relative importance) 66.67% 33.33%      144 Table B-2 Prioritizing product characteristics using Lyman's Normalization Method: an exaggerated example  Product Characteristics (or technical characteristics or design requirements) (HOWs)   Product Characteristics Type 1 Product Characteristics Type 2 Customer Requirements (WHATS) Weights of  WHATs (di) Deck Overlay Approach Slab Overlay Alkali Silica Reaction (ASR) Expansion Joints Paint on Steel Concrete Coatings Handrails Sidewalk Wingwalls Culvert Deck Flags/Signs Improved Surface Conditions 20.00% 0 0 0 0 9 9 9 9 9 9 9 9 Enhanced Aesthetics of Bridge 80.00% 9 9 9 9 0 0 0 0 0 0 0 0 Individual Weight (wj) 20 20 20 20 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 Total weights of HOWs (absolute importance) 80 20 Total weights of HOWs (relative importance) 80.00% 20.00%     145 Table B-3 Prioritizing product characteristics using Wasserman's Normalization Method: an exaggerated example  Product Characteristics (or technical characteristics or design requirements) (HOWs)   Product Characteristics Type 1 Product Characteristics Type 2 Customer Requirements (WHATS) Weights of  WHATs (di) Deck Overlay Approach Slab Overlay Alkali Silica Reaction (ASR) Expansion Joints Paint on Steel Concrete Coatings Handrails Sidewalk Wingwalls Culvert Deck Flags/Signs Improved Surface Conditions 20.00% 0 0 0 0 0.1 0.1 0.1 0.1 0.1 0.19 0.19 0.1 Enhanced Aesthetics of Bridge 80.00% 0.284 0.25 0.22 0.25 0 0 0 0 0 0 0 0 Individual Weight (wj) 23 20 18 20 2 2 2 2 2 4 4 2.5 Total weights of HOWs (absolute importance) 80 20 Total weights of HOWs (relative importance) 80.00% 20.00%     146 Table B-4 Matrix of correlations between product characteristics (HOWs) in the scale [0,1]: an exaggerated example γ j k≈γk j  Deck Overlay Approach Slab Overlay Alkali Silica Reaction (ASR) Expansion Joints Paint on Steel Concrete Coatings Handrails Sidewalk Wingwalls Culvert Deck Flags/Signs Deck Overlay 1 0.3 0.9 0.3 0 0 0 0 0 0 0 0 Approach Slab Overlay 0.3 1 0 0.9 0 0 0 0 0 0 0 0 Alkali Silica Reaction (ASR) 0.9 0 1 0 0 0 0 0 0 0 0 0 Expansion Joints 0.3 0.9 0 1 0 0 0 0 0 0 0 0 Paint on Steel 0 0 0 0 1 0 0 0 0 0 0 0 Concrete Coatings 0 0 0 0 0 1 0 0 0 0 0 0 Handrails 0 0 0 0 0 0 1 0 0 0 0 0 Sidewalk 0 0 0 0 0 0 0 1 0 0 0 0 Wingwalls 0 0 0 0 0 0 0 0 1 0 0 0 Culvert 0 0 0 0 0 0 0 0 0 1 0.9 0 Deck 0 0 0 0 0 0 0 0 0 0.9 1 0 Flags/Signs 0 0 0 0 0 0 0 0 0 0 0 1 TOTAL 2.50 2.20 1.90 2.20 1.00 1.00 1.00 1.00 1.00 1.90 1.90 1.00   147 Appendix C  : Microsoft Excel Visual Basic Application (VBA) Code for Hidden Markov Implementation  Sub Macro1() Dim cell As Excel.Range 'Dim counter1 As Double Dim OLR As Integer Dim ORR As Integer Dim LR As Integer Dim RR As Integer Dim Rng1 As Range Dim Rng1a As Range Dim Rng2 As Range Dim Rng3 As Range Dim Rng4 As Range Dim Rng5 As Range Dim WF As Object Dim Av As Variant Dim xarray As Variant Dim yarray As Variant Dim yarray1 As Variant Dim yarrayIn As Variant Dim yarrayOut As Variant Dim zarray As Variant Dim zarray1 As Variant Dim ab As Range Dim ws As Worksheet Dim i As Integer Dim n As Double Dim m As Integer Dim u As Integer Dim counter2 As Integer Dim counter3 As Integer Dim invRowSt As Integer Dim invRowEnd As Integer Dim s As Long Dim pow As String Dim LR1 As Integer Dim RR1 As Integer Dim invRowSt1 As Integer Dim invRowEnd1 As Integer  Sheets("Step-1").Select   148            For counter2 = 0 To 150 Step 30          'counter3 = counter2 / 10                For counter1 = 49 To 73 Step 6              'Set Rng1 = Range(Cells(counter1, 5), Cells(counter1 + 3, 7))     OLR = 957 + counter1 + counter2     ORR = 959 + counter1 + counter2     LR = counter1 - OLR     RR = counter1 + 4 - ORR     invRowSt = 4 + (counter2 / 10)     invRowEnd = 6 + (counter2 / 10)     Set WF = Application.WorksheetFunction     Range(Cells(OLR, 1), Cells(ORR, 3)).Select     Selection.FormulaArray = "=MINVERSE(R[" & LR & "]C[" & invRowSt & "]:R[" & RR & "]C[" & invRowEnd & "])"             ' B-Inverse*A**n          xarray = Range(Cells(OLR, 1), Cells(ORR, 3)).Value       pow = Cells(14, 4).Value  ' Fetch matrix from sheet      yarrayIn = Range(Cells(counter1 - 3, 5 + counter2 / 10), Cells(counter1 - 1, 7 + counter2 / 10)).Value     yarrayOut = yarrayIn If pow = 1 Then GoTo 73 For s = 1 To pow - 1       yarrayOut = WorksheetFunction.MMult(yarrayIn, yarrayOut) Range(Cells(2000 + counter2, 4), Cells(2002 + counter2, 6)).Value = yarrayOut Next s 73:     zarray = WF.MMult(xarray, yarrayOut)     149     Range(Cells(OLR, 4), Cells(ORR, 6)).Value = zarray  ' (B-Inverse*A**n)*B              xarray = Range(Cells(OLR, 4), Cells(ORR, 6)).Value     yarray = Range(Cells(counter1, 5 + counter2 / 10), Cells(counter1 + 2, 7 + counter2 / 10)).Value     zarray = WF.MMult(xarray, yarray)     Range(Cells(OLR, 8), Cells(ORR, 10)).Value = zarray      ' (B-Inverse*A**n)*B*A          xarray = Range(Cells(counter1 - 3, 5 + counter2 / 10), Cells(counter1 - 3, 7 + counter2 / 10)).Value     yarray = Range(Cells(OLR, 8), Cells(ORR, 10)).Value     zarray = WF.MMult(xarray, yarray)     Range(Cells(OLR, 12), Cells(ORR, 14)).Value = zarray  ' (B-Inverse*A**n)*B*A*States      LR1 = OLR + LR - 3     xarray = Range(Cells(OLR, 8), Cells(ORR, 10)).Value     yarray = Range(Cells(21, 4), Cells(23, 4)).Value     zarray = WF.MMult(xarray, yarray)     yarray1 = Range(Cells(LR1, 2), Cells(LR1, 4)).Value     zarray1 = WF.MMult(yarray1, zarray)     Range(Cells(OLR, 16), Cells(OLR, 16)).Value = zarray1          '     'zarray = WF.MMult(yarray, zarray)                   For u = 0 To 4                  If u = 0 Then m = 0 Else m = u + 5 * u                     n = Range(Cells(1006 + counter2 + m, 16), Cells(1006 + counter2 + m, 16)).Value            Range(Cells(46 + u, 24 + counter2 / 30), Cells(46 + u, 24 + counter2 / 30)).Value = n          Next u  Next counter1    150 Next counter2   Range("X50").Select  ActiveWorkbook.Save  End Sub 

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