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Two types of preventive maintenance policies are considered. A policy is defined to be optimum if it maximizes “limiting efficiency,” i.e., fractional amount of up-time over long intervals. Elementary renewal theory is used to obtain optimum policies. The optimum policies are determined, in each case, as unique solutions of certain integral equations depending on the failure distribution. It is shown that both solutions are also minimum cost solutions when the proper identifications are made. The two optimum policies are compared under certain restrictions.

The theory of binary coherent systems is generalized for multi-state components. The system state is defined to be the state of the “worst” component in the “best” min path, or equivalently, the state of the “best” component in the “worst” min cut. Many of the results for the binary case can be computed for multi-state systems using the binary structure and reliability function concepts. Monotonicity results are now valid with respect to stochastic ordering of component probability vectors.

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