Repairable systems availability optimization under imperfect maintenance

This paper deals with the modeling of a preventive maintenance strategy applied to a single-unit system subject to random failures. According to this policy, the system is subjected to imperfect periodic preventive maintenance restoring it to 'as good as new' with probability p and leaving it at state 'as bad as old' with probability q. Imperfect repairs are performed following failures occurring between consecutive preventive maintenance actions, i.e the times between failures follow a decreasing quasi-renewal process with parameter a. Considering the average durations of the preventive and corrective maintenance actions as well as their respective efficiency extents, a mathematical model is developed in order to study the evolution of the system stationary availability and determine the optimal PM period which maximizes it. The modeling of the imperfection of the corrective maintenance actions requires the knowledge of the quasi-renewal function. A new expression approximating this function is proposed for systems whose times to first failure follow a Gamma distribution. Numerical results are obtained and discussed.