Imperfect Preventive Maintenance Policies with Unpunctual Execution

Traditional maintenance planning problems usually presume that preventive maintenance (PM) policies will be executed exactly as planned. In reality, however, maintainers often deviate from the intended PM policy, resulting in unpunctual PM executions that may reduce maintenance effectiveness. This article studies two imperfect PM policies with unpunctual executions for infinite and finite planning horizons, respectively. Under the former policy, imperfect PM actions are periodically performed and the system is preventively replaced at the last PM instant. The objective is to determine the optimal number of PM actions and associated PM interval so as to minimize the long-run average cost rate. However, the latter policy specifies that a system is subject to periodic PM activities within a finite planning horizon and there is no PM activity at the end of the horizon. The aim is then to identify the optimal number of PM activities to minimize the expected total maintenance cost. In this article, we discuss the modeling and optimization of the two unpunctual PM policies and then explore the impact of unpunctual executions on the optimal PM decisions and corresponding maintenance expenses in an analytical or numerical way. The resulting insights are helpful for practitioners to adjust their PM plans when unpunctual executions are anticipated.