有两种故障状态的两部件串联系统的预防维修策略

本文研究的是由两个部件串联组成且有两种故障状态的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态。每个部件发生故障都有两种状态, 可维修和不可维修。当部件的故障为可维修故障时, 修理工对其进行故障维修, 且每次故障维修后的工作时间形成随机递减的几何过程, 每次故障后的维修时间形成随机递增的几何过程。当部件发生N次可维修故障或一次不可维修故障时进行更换。以部件进行预防维修的间隔和更换前的可维修故障次数N组成的二维策略(T, N) 为策略, 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, 并给出了具体例子和数值分析。

The Preventive Maintenance Policy for a Two-component Series System with Two Types of Failures

In this paper,we study the preventive maintenance policy for a two-component series system with two types of failures.When the working time of the system reaches,the system will be preventively repaired,and the preventive maintenance will restore every component to the state which is the same as the last failure repair.The system has two types of failures,one is repairable,the other is unrepairable.When the repairable failure occurs,the system will be repaired by the repairman,the successive survival times of the component will form a stochastically decreasing geometric process and the consecutive repair times after component failures will form a stochastically increasing geometric process.The system will be replaced by a new and identical one at the time following theth repairable failure or once unrepairable failure.We look for a bivariate policy,whoseis the time interval of two consecutive preventive maintenance,is the repairable failure time of the component before replacement.By using the renewal process theory and geometric process theory,the explicit expression of the long-run expected cost per unit time is derived.Finally,a numerical example is given.