修理工多重休假且修理设备可更换的κ/n(G)表决可修系统研究

Study on a k-out-of-n:G repairable system with multiple vacations and one replaceable repair facility

本文将"修理工多重休假"机制和"修理设备可发生失效且可更换"策略同时引入到k/n(G)表决可修系统中,利用马尔可夫过程理论求得了系统处于各状态的稳态概率的递推表达式.在此基础上,给出了系统的稳态可用度、首次故障前平均时间、稳态故障频度、修理工繁忙的稳态概率、修理设备的稳态不可用度、故障部件的平均数目以及故障部件的平均等待修理时间等一系列性能指标.最后以6/10(G)表决可修系统为例,分析了修理工的休假率和修理设备的失效率对几个主要性能指标的影响.

In this paper, a k-out-of-n：G repairable system with a repair facility and one repairman who takes multiple vacations is studied. By using the Markov analysis method, we obtain the recursive ex- pressions for the stationary state probabilities of our repairable system. Furthermore, some important performance characteristics such as the steady-state availability of the system, mean time to the first failure, failure frequency of the system, the probability for the repairman being busy, the steady-state unavailability of the repair facility, the expected number of failed components and the expected waiting time of failed components are derived. Finally, we present a special case of 6-out-of-10：G repairable system and study the influence of the vacation rate of repairman and the failure rate of repair facility on several performance characteristics.