This article considers an optimal maintenance policy for the multistate systems with the finite number of states. Each state is described by its level of performance ranging from the perfect one to the zero level for the state of failure. Moreover, we assume that the cost of preventive maintenance (PM; i.e., repair/rejuvenation in our case) also depends on the state of a system. Based on the proposed policy, the expected cost per unit of time is defined and the conditions for the existence of the unique and finite PM time are obtained in terms of dynamic reliability characteristics of the system. The results are applied to the three-state Markovian system and a parallel system with n components. The latter is also discussed for the case of the positively dependent components.

中文翻译：

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具有状态相关维修成本的退化多态系统的优化维护

本文考虑具有有限状态数的多状态系统的最优维护策略。每个状态都由其性能级别来描述，从完美的一级到故障状态的零级。此外，我们假设预防性维护（PM；即我们案例中的修复/恢复）的成本也取决于系统的状态。基于所提出的策略，定义了单位时间的期望成本，并根据系统的动态可靠性特性获得了唯一且有限的PM时间存在的条件。将结果应用于三态马尔可夫系统和具有n 个分量的并行系统。后者也针对正相关组件的情况进行了讨论。