Optimal quasi-periodic preventive maintenance policies for a repairable system with stochastic maintenance interval

The usual preventive maintenance (PM) of a repairable system is done before failure at integer multiples of time T. In some real cases, PM cannot be performed as soon as a planned PM period is reached because of effects of some random factors, while it is usually done within an implemented period, and thus it makes the PM period become a stochastic interval. From this viewpoint, a quasi-periodic imperfect preventive maintenance policy is proposed in this paper, in which a repairable system experiences either a minor failure or catastrophic failure when a failure occurs, and the first (N-1) PM intervals is divided into a planned PM period and an implemented period. In the former, the system may be suffered an unplanned PM for removing a catastrophic failure and performing a PM, whereas in the latter, the system is preventively maintained following an occurrence of a catastrophic failure or a dynamic PM plan, whichever comes first. At the Nth PM interval, the system is replaced either when a catastrophic failure occurs or operational time reaches T, whichever comes first. An optimization of the proposed mode is introduced, the existence and the uniqueness of the optimal solution are presented, and a useful constraint of the implemented period is obtained. Finally, a real case study of PM on Chinese diesel locomotives is examined to illustrate the proposed maintenance policy.