研究由两个部件串联组成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. 当部件发生故障后进行故障维修, 因为各种原因可能会延迟修理. 部件在每次故障维修后的工作时间形成随机递减的几何过程, 且每次故障后的维修时间形成随机递增的几何过程. 以部件进行预防维修的间隔T和更换前的故障次数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.

In this paper, we study the preventive maintenance policy for a two-component series system. When the working time of the system reaches T, the system will be preventive repaired. The preventive maintenance restores every component to the state which is the same as the last failure repair. When the failure occurs, the repair may be delayed for every component. The successive survival times of the component form a stochastically decreasing geometric process and the consecutive repair times after component failures form a stochastically increasing geometric process. We look for a bivariate policy (T,N), which T is the working time of the system before preventive maintenance, N is the 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.