Systems commonly operate under time-varying environmental condition (EC). Since the EC can affect the degradation process of a system, maintenance planning can be quite challenging. This study focuses on a case where the evolution processes of the system degradation and the EC are governed by Markov processes, for which the transition rate matrix of degradation states varies with the EC. To maintain the system, an inspection/maintenance policy is adopted, where a maintenance action is carried out immediately when a failure occurs during an inspection interval or upon an inspection epoch when the system’s degradation state reaches a certain threshold. Imperfect maintenance (IM) and replacement are considered in this study, where a certain number of consecutive IM actions can be carried out before each replacement. We first derive the long-run average cost based on the semi-regenerative properties of the system, and then jointly determine the inspection interval, preventive maintenance threshold and number of IM actions before a replacement by minimizing the long-run average cost. A numerical study is conducted to demonstrate the proposed maintenance policy.

系统通常在时变环境条件（EC）下运行。由于EC会影响系统的降级过程，因此维护计划可能会非常具有挑战性。本研究的重点是系统退化和EC的演化过程受马尔可夫过程支配的情况，对于这种情况，退化状态的转换率矩阵随EC的变化而变化。为了维护系统，采用了检查/维护策略，当在检查间隔期间发生故障时立即执行维护操作，或者当系统的退化状态达到特定阈值时在检查周期之后立即执行维护措施。在这项研究中考虑了不完善的维护（IM）和更换，在每次更换之前，可以执行一定数量的连续IM动作。我们首先根据系统的半再生特性得出长期平均成本，然后通过使长期平均成本最小化，共同确定更换前的检查间隔，预防性维护阈值和IM操作数量。进行了数值研究，以证明建议的维护策略。