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.

中文翻译：

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不按时执行的不完善的预防性维护政策

传统的维护计划问题通常假设预防性维护 (PM) 策略将完全按计划执行。然而，实际上，维护人员经常偏离预期的 PM 策略，导致不准时的 PM 执行，这可能会降低维护效率。本文分别研究了两种不完美的 PM 策略，它们分别在无限和有限的规划范围内不准时执行。在前一种策略下，不完善的 PM 动作会定期执行，并在最后一个 PM 时刻预防性地更换系统。目标是确定 PM 操作的最佳数量和相关的 PM 间隔，以便最小化长期平均成本率。然而，后一种策略指定系统在有限的规划范围内受到周期性 PM 活动的影响，并且在范围结束时没有 PM 活动。然后，目标是确定 PM 活动的最佳数量，以最小化预期的总维护成本。在本文中，我们讨论了两种不准时 PM 策略的建模和优化，然后以分析或数值的方式探讨不准时执行对最优 PM 决策和相应维护费用的影响。由此产生的见解有助于从业者在预计不准时执行时调整他们的 PM 计划。我们讨论了两种不准时 PM 策略的建模和优化，然后以分析或数值的方式探讨不准时执行对最佳 PM 决策和相应维护费用的影响。由此产生的见解有助于从业者在预计不准时执行时调整他们的 PM 计划。我们讨论了两种不准时 PM 策略的建模和优化，然后以分析或数值的方式探讨不准时执行对最佳 PM 决策和相应维护费用的影响。由此产生的见解有助于从业者在预计不准时执行时调整他们的 PM 计划。