具有一般预防性维修结果的一个几何过程模型

本文研究单部件和一个修理工组成的可修系统．在系统故障前考虑了预防维修，且假设预防维修的结果是系统相当于已被使用了一段时间Ｙ，则Ｙ是一随机变量，我们称Ｙ是系统的已有年龄，它的分布函数是一个与该系统维修前已使用时间有关的一般分布，即Ｐｒ｛Ｙ≤ｙ｜ｘ｝＝Ｈ（ｙ｜ｘ），ｘ是系统维修前的已使用时间．而当系统故障时维修结果为“修复非新”，这样，我们利用几何过程，以系统的故障次数Ｎ为更换策略，选择最优的Ｎ＊，使得系统经长期运行后单位时间内的期望费用达到最小．最后，对系统寿命服从指数分布的情形，给出了已有年龄Ｙ的分布，并给出了数值例子．

A Geometric Processes Model with General Preventive Maintenance Result

This paper studies the repairable system which consists of a unit and a repair worker. We consider preventive maintenance before the failure of the system, assuming that the result of preventive maintenance is equivalent to a used life Y of the system, Y being a random variable. Its probability distribution function is a general one relating only to the time for which the system has worked before failure. When the repaired unit is not good as the new one, we apply the geometric processes, and take the failure numbers N as the replacemat polied. We obtain the optimum N * , where the minimal unit time expected cost of the system long run is achieved. Finally for the case of exponential distribution of the life, the distribution of the used life Y is given and a numerical example is also presented.