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An optimal replacement policy for a three-state repairable system with a monotone process model

机译：具有单调过程模型的三态可修复系统的最优替换策略

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摘要

In this paper, a deteriorating simple repairable system with three states, including two failure states and one working state, is studied. Assume that the system after repair cannot be "as good as new", and the deterioration of the system is stochastic. Under these assumptions, we use a replacement policy N based on the failure number of the system. Then our aim is to determine an optimal replacement policy N* such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. An explicit expression of the average cost rate is derived. Then, an optimal replacement policy is determined analytically or numerically. Furthermore, we can find that a repair model for the three-state repairable system in this paper forms a general monotone process model. Finally, we put forward a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.
机译：本文研究了一种具有三个状态的恶化的简单可修复系统，其中包括两个故障状态和一个工作状态。假定修复后的系统不能“像新系统一样好”，并且系统的退化是随机的。在这些假设下，我们基于系统的故障编号使用替换策略N。然后，我们的目标是确定最佳更换策略N *，以使平均成本率（即每单位时间的长期平均成本）最小化。得出平均成本率的明确表达。然后，通过分析或数值确定最佳替换策略。此外，我们发现本文中的三态可修复系统的修复模型形成了一般的单调过程模型。最后，我们给出了一个数值例子，并对模型进行了一些讨论和敏感性分析。

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