A Study on an Optimal inspection Policy for Deterioration and Failure System

我们报告了2002年和2003年财政年度执行的研究大纲。假设，维修活动是强制性的任意性是一般的。然而，实际上存在各种限制，并且难以任意地执行维护活动。另一方面，在多个部件组成的系统中，故障机理通常被认为是多个因素的组合。构件失效不仅是由于构件本身的劣化，也是由于相邻构件的失效引起的。我们用随机过程的方法对这些问题提出了一些理论模型。作为一个典型的例子，我们得到了一个预期的维护主机每单位时间在无限的时间范围内。以期望费用率为准则函数，讨论了以期望费用率最小为目标的最优维修策略。研究了由离散时间失效单元和马尔可夫退化单元组成的系统，给出了系统最优解存在的条件。将最优检验和更换问题表示为带折扣的马尔可夫决策过程。分析了最优策略的结构，阐明了面积策略的最优性。

We report the outline of the research executed in 2002 and 2003 fiscal year.Assumption that the maintenance activity is enforceable at arbitrariness is general. However, various restrictions actually exist, and it is difficult to execute the maintenance activity at arbitrariness. We paid attention to maintenance opportunity that can maintain the system.On the other hand, in more than one component systems, failure mechanism is usually considered as a combination of several factors. The component fails not only due to its own deterioration, but also being caused by the failure of adjacent component. We proposed some theoretical models to these problems by using stochastic processes. As a typical instance, we derived an expected maintenance host per unit time over infinite time horizon. The function as a criteria function for decision making, we discussed optimal maintenance policies to minimize the expected cost rate. As a result, the condition of the existence of the optimum solution was able to be led.The system which consisted of the discrete time failure unit and Markov-deterioration unit was considered. The optimal inspection and replacement problem was formulated as a Markov decision process with a discount. The structure of the optimal policy was analyzed, and the optimality of the area policy was clarified.