UBC Theses and Dissertations
On optimization in probabilistic design Tutek, Mehmet N.
In classical design the inputs to the design process, namely the relevant material property M and the load L are taken as deterministic values. The probabilistic design approach recognizes the variation in design inputs, and the consequent random behavior of these variables. The material property varies from one lot of production to another and within the same production lot. The applied load to a particular specimen varies widely within some range. The design output, a dimensional parameter A, also varies within the given range of tolerances, and therefore is randomly distributed among specimens. Failure occurs at the first instance the load value L is larger than the resisting strength of the material, S. Among n load applications the first exceedance of S by L results in failure. The relevant load variable is therefore the extreme value of a number n of loads that correspond to a given design mission time. Within this framework, design reliability and mission time emerge as the appropriate design inputs. In probabilistic design the designer has a wide range of choice for both input parameters, reliability R and mission time n. In this Thesis, the optimal combination of n and R is determined in a logical way. A cost-benefit analysis is made, resulting in an optimal combination using the benefit and cost to the decision maker. Since benefit is relative, the information required to determine the benefit function is acquired from the decision maker through several questions and a "reference gamble". Cost is analyzed and a cost function is constructed. Using the benefit and cost functions, indifference and constant cost functions are derived, resulting in suboptimal combinations of R and n. The optimal combination is chosen among the suboptimal combinations by minimizing the cost-benefit ratio. An example is presented to illustrate this decision model.
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