STANFORD UNIV CA
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Coherent structure function theory is an axiomatic approach to reliability in which the components and systems are binary, i.e., they have two states - operational and failed. The first part of the thesis extends the theory to components and systems with multiple states. This is useful for modeling systems in which partial failure may occur. Multistate coherent structure functions are defined, and it is shown that most of the binary results have multistate analogs. These results deal with duals, modules, minimum cut and path sets, reliability importance, reliability bounds, closure theorems, fault trees, and block diagrams. The theory is further extended to allow each component and the system to have a continuum of states. Optimal maintenance policies for periodically inspected multistate components have previously appeared in the literature. The second part of the thesis extends those policies to continuously monitored equipment by using Markov decision processes and continuous time Markov chains. The main theorems are in the form of control limit rules which state that it is optimal to repair or replace a component whenever it has degraded to a certain level. It is shown that under certain assumptions the optimal policy is to repair the component as much as possible. Equivalences between shock models, continuous time models, and discrete time models are discussed.
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