Research of the expected downtime for repairable system with single repairman vacation

To study one unit repairable system with single repairman vacation,a kind of new maintenance and replacement model is proposed.Supposing that the system is repairable,the successive survival time of the system constitutes a decreasing geometric process stochastically,while the consecutive repair time of the system constitutes an increasing geometric process.Under the conditions that the repairman vacation time is respectively random variable and constant,replacement policy is considered based on the working age T and the failure number N for the system and the long-run expected downtime per unit time as objective function is chosen,and mathematic models is established by using renewal process and geometric process theory,the explicit expressions of the objective function are derived.According to the difference of objective functions,the optimal replacement policy T~* and N~* are obtained by minimizing the objective function or setting downtime limit.Finally,two simulation examples are given to validate the effectiveness of the proposed method.