修理设备可修理的几何过程模型的最优维修策略

The optimal maintenance policy for the geometric process model with a repairable repair facility

本文研究了一个修理设备在工作过程中可能发生故障且可以被修理的系统的维修策略．当系统发生故障时用修理设备对其进行故障维修，修理设备在维修过程中也可能发生故障，并有修理工对修理设备进行维修．当修理设备恢复正常后继续对系统进行维修．系统和修理设备逐次故障维修后的工作时间都形成随机递减的几何过程，且逐次故障后的修理时间都形成随机递增的几何过程．当系统的故障次数达到N时对系统和修理设备都进行更换，利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式，证明了最优策略的存在性和唯一性，并给出了具体例子和数值分析．

In this paper, the optimal maintenance policy is investigated for a system with repairable repair facility. When the system fails, it will be repaired by the repair facility. The repair facility may be subject to failure during the repair period, and it can be repaired by a repairman if it fails. The successive survival times of the system and repair facility form different stochastically decreasing geometric processes respectively, and the consecutive repair times after failures of the system and repair facility form different stochastically increasing geometric processes respectively. When the failure number of the system reaches an integer number N, the system and repair facility will be replaced by a new and identical one. By using the renewal process theory and geometric process theory, the explicit expression of the long-run average cost per unit time under policy N is derived, and the corresponding optimal replacement policy can be found analytically. It is proved that the optimal replacement policy exists uniquely. Finally, the numerical examples are given.