一个可修系统的最优更换模型

本文考虑了单部件、一个修理工组成的可修系统，在故障系统不能“修复如新”的前提下，我们利用几何过程，以系统年龄Ｔ为策略，选择最优的Ｔ使得系统经长期运行单位时间的期望效益达到最大．本文还在一定的条件下证明了最优更换策略Ｔ的唯一存在，且求出了系统经长期运行单位时间的最大期望效益的明显表达式．

An Optimal Replacement Model for the Repairable System

This paper considers a repairable system consisting of one component and a single repairman. Assume that the system after repair is not"as good as new". Under this assumption, by using the geometric process we consider the replacement policy T based on the age of the system. The problem is to determine the optimal replacement policy T* such that the long-run expected benefit per unit time is maximized. Therefore, in some conditions, the existence and uniqueness of the optimal policy T* can be proved, and the explicit expression of the maximum of the long-run expected benefit per unit time can be found , too.