A repair-replacement policy for a system subject to missions of random types and random durations

Increasing research efforts have been devoted to mission-oriented preventive maintenance (PM) policies that are restricted mainly to certain missions. This paper investigates the optimization problem of a repair -replacement policy for systems subject to intermittent missions of random types and random durations, which is more realistic in practice. When a mission is completed, the system is assigned a new mission with the type dependent on the previous type and the duration following a general distribution. The randomness of missions affects the failure rate of the system, the penalty for failed missions, and the schedules of PM actions. Taking advantage of the shutdown opportunity of switching missions, the decision maker determine among three possible actions: do-nothing, preventive repair, and preventive replacement to minimize the long-run average cost rate. The optimization problem is formulated as a semi-Markov decision process and is solved by the policy iteration algorithm. An extended policy involving two monotonic control limits is proposed and optimized by a modified policy iteration algorithm. Two numerical examples illustrate the effectiveness of the proposed approach.