A reliability-driven preventive maintenance scheduling problem

In this study, we investigate the Preventive Maintenance (PM) schedules for a system subject to failure. Our concern is to find the optimal intervals between the PM activities. We assume that the operating cost of the system linearly increases dependent on the cumulative failure rate of the system since the last PM. The expected costs of repair and PM are different from one another. The durations of these activities are also different. We assume that the duration of repair is dependent on the cumulative failure rate. Whenever the system reliability reaches the reliability threshold R, an imperfect PM is performed, which leads to a gradual decrease in maintenance intervals. We formulate the problem of finding the maintenance intervals. We provide the optimal solution based on analysis of the problem using the reliability threshold value.