A complex device, like a jet engine or an electronic computer, is composed of hundreds of major components that require maintenance. The determination of the reliability and the optimal maintenance policy for such systems is further complicated by the dependence among interacting components. Component lifetimes are generally stochastically dependent due to the fact that they all function under the same environmental conditions like temperature, humidity, and vibrations. Moreover, they are also economically dependent since it is possible to do preventive maintenance to functioning components at marginal, additional cost, while failed components are being maintained. We discuss the effects of these dependencies on periodic replacement policies, and provide useful characterizations of the optimal replacement policy. The formulation involves a sample path analysis of the reliability system which leads to the utilization of Markov decision theory. Interesting intuitive and counterintuitive results are presented.
The lifetimes of the components of a device depend on each other because of their joint dependence on the environmental conditions. We introduce intrinsic age processes, one for each component, to handle such dependence. The data required can be obtained by experiments under controlled laboratory conditions. The computations needed for randomly varying conditions are recursive and can be used for making decisions regarding maintenance and replacement.
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