Traditional reliability methods describe systems as binary, but real life systems usually have multiple states of operation that describe more accurately their performance. The computation of reliability for complex systems modeled by multiple multi-state components is critical for engineers, researchers and scientists, but the computational complexity grows as the number of components increase. This research presents models and methods that allow the system designer to determine the reliability of a multi-state system based on individual reliabilities of multi-state components. Equivalence classes are used with minimal conjunction and minimal disjunction in order to compute the system reliability. This helps with the reduction of computations in most cases by finding vectors that dominate states of the system instead of performing computations using all the states of the system, and it also captures sensitivity of the reliability of the system due to the performance of some components. Dynamic reliability bounds are also presented for multi-state systems with multi-state components using an iterative process. Bounds are more convenient for large systems because finding the exact reliability is computationally a very hard problem. Systems considered in this research can degrade to any lower state at the system level and also at the component level. An application is presented for a simple flow transmission system. The analysis becomes very complex even for a system with few components with small number of states. Customer-centered models are presented using homogeneous continuous time Markov processes. System designers are interested in evaluating systems based on preferences of the customers. Utility and disutility functions reflecting the preference of the customer towards certain system-performance levels are presented and superimposed in models for decision analysis and risk management.
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