不计预防维修时间的一个最优更换策略

An Optimal Replacement Policy Taking no Account of the Preventive Repair Time

本文研究了单部件一个修理工组成的可修系统，为延长系统的使用寿命，在系统故障前考虑了预防维修，如果假定预防维修能“修复如新”且不计预防维修时间，而故障维修为“修复非新”时，我们利用单调的几何过程，以系统的故障次数Ｎ为更换策略，目的是选择最优的Ｎ＊，使得系统经长期运行单位时间的期望损失达到最小，我们不仅求出了该期望损失的解析表达式，而且对该系统的预防维修的定长间隔时间Ｔ及更换策略Ｎ进行了讨论．

In this paper, a repairable system consisting of one compon and one repairman is studied. In order to prolongating the working time of the system, the preventive reair before the system failure is consider and assume that it can be“as good as new” but the preventive repair time is negligible, while repair after the system failure is not“as good as new”. Under this assumption, by uisng the monotone geometric process, we consider the replacement policy N based on the number of failure of the system. Our problem is to be determined: the optimal replacement policy N * such that the long-run expected cost per unit time is miniminxed. The explicit expression of the long-run expected cost per unit time is derived, and some problems for the length of fixed time of the preventive repair and the replacement policy of the syestem are discussed.