Optimal periodic preventive maintenance policies under uncertainty

This paper deals with a one-unit system with three states: Normal, wear-out and failure. While the hazard rate is a constant in the normal state, it is monotonically increasing and unbounded in the wear-out state. Periodic preventive maintenance (PM) in the wear-out period is carried out with probability q, restoring the system to its normal state. After N-1 consecutive periods of non-PM, a preventive replacement is made at the end of the Nth period. On failure, an (unplanned) replacement is made. Apart from explicit expressions for the expected cost per unit time, conditions for the existence and uniqueness of the optimal period T* and optimal number N* are obtained.