关键词: 更新过程, 几何过程, 故障维修, 预防维修, 期望费用

Abstract: 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.

Key words: renewal process, geometric process, failure repair, preventive maintenance, expected cost