Cost minimization for periodic maintenance policy of a system subject to slow degradation

This paper considers a repairable system which undergoes preventive maintenance (PM) periodically and is minimally repaired at each failure. Most preventive maintenance models assume that the system improves at each PM so that the hazard rate is reduced to that of a new system or to some specified level. In this paper, we consider the situation where each PM relieves stress temporarily and hence slows the rate of system degradation, while the hazard rate of the system remains monotonically increasing. The optimal number and period for the periodic PM that minimize the expected cost rate per unit time over an infinite time span are obtained. We also consider the case when the minimal repair cost varies with time. Explicit solutions for the optimal periodic PM are given for the Weibull distribution case.