An age reduction approach for finite horizon optimization of preventive maintenance for single units subject to random failures

We consider a single unit working in a continuous mode of operation characterized by an increasing failure rate. We determine the optimal number of preventive maintenance activities to be scheduled within a time horizon of interest, the required extent of the preventive maintenance by means of an age reduction of the unit and the corresponding optimal value of the expected profit. We assume that any breakdown occuring is minimally repaired, the repair is performed instantaneously, and the repair cost is the same for any repair. On the other hand, the cost associated with a preventive maintenance activity may vary as well as its duration.