Two-stage maintenance of a production system with exponentially distributed on and off-periods

We consider an on–off production system which is subject to failure during on-periods. In case of a failure, the production system is maintained correctively. In addition, preventive maintenance is carried out to prevent failures. The costs of both preventive and corrective maintenance are modelled in terms of the net down-time of the production system, that is, the time that the system is not available when needed for production. Since preventive maintenance can be planned during off-periods, there is a perspective of significant savings if some freedom is built in concerning the starting time of preventive maintenance. Therefore, a two-stage maintenance policy is considered, which—in a first stage—provides the maintenance manager with a finite interval during which preventive maintenance must be carried out, and—in a second stage—determines the optimal starting time for preventive maintenance within this interval. Computational results offer useful insights, and indicate that significant savings can be achieved in comparison with a classical age maintenance policy.