Optimal planning of unpunctual preventive maintenance

In traditional maintenance decision-making, maintenance planners assume that their prescribed Preventive Maintenance (PM) policies will be implemented without error. In practice, however, the individuals responsible for implementing such plans often deviate from the intended PM policy, resulting in unpunctual PM actions. We formulate cost-rate minimizing models to investigate the impact of such deviations, assuming that the actual PM time differs from the scheduled PM time in a probabilistic manner. We establish both analytical and numerical results for two specific types of maintenance policies, namely, age replacement with and without minimal repair.