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UBC Theses and Dissertations

Reliability and maintenance for interrelated systems Armstrong, Michael John


In this paper we consider three topics in reliability and maintenance. Their common feature is the explicit consideration of interdependence, either amongst components within a machine, amongst stages in a logistics chain, or amongst machines sharing maintenance facilities. Chapter 1 examines measures of the contribution of a component towards a system's reliability; these measures include structural importance, marginal reliability importance, joint reliability importance, and link importance. We review these different measures and examine how they relate to each other. We show that some structural results previously derived for independent components continue to hold for associated components. We then propose extensions to each importance measure to cover components which have two failure modes rather than the conventional one, and show that these extensions largely retain the properties of the original definitions. Chapter 2 examines a system containing one machine subject to random failure, for which we wish to determine a maintenance policy and a spare ordering policy. We consider the solvability and desirability of jointly optimizing these two traditionally separate policies. We discuss why the general form of the problem is intractable and show how it might be approached using bounds and heuristic policies; more importantly, we examine several special cases which are more tractable. Particular attention is paid to systems which contain only one spare at a time; we show that these systems have some convexity properties which facilitate cost minimization. We subsequently consider systems which allow more than one spare, but make use of other restrictions or assumptions to simplify analysis. Chapter 3 examines how to coordinate maintenance for machines sharing repair facilities, a task which is commonly called the machine repairman problem. Existing studies of this problem make the restrictive assumption that repairs are performed only after machine failure; our work extends the machine repairman model by allowing preventive repair. We derive analytical results for a single critical age repair policy, and then use numerical studies to investigate other heuristic policies which can improve the system's cost effectiveness.

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