On Optimal Maintenance of Degrading Multistate Systems With State-Dependent Cost of Repair

Abstract

This article considers an optimal maintenance policy for the multistate systems with the finite number of states. Each state is described by its level of performance ranging from the perfect one to the zero level for the state of failure. Moreover, we assume that the cost of preventive maintenance (PM; i.e., repair/rejuvenation in our case) also depends on the state of a system. Based on the proposed policy, the expected cost per unit of time is defined and the conditions for the existence of the unique and finite PM time are obtained in terms of dynamic reliability characteristics of the system. The results are applied to the three-state Markovian system and a parallel system with n components. The latter is also discussed for the case of the positively dependent components.