研究了修理工多重休假且修理设备可更换的$n$中取$k$温贮 备可修系统的瞬态可靠性指标, 其中部件的贮备寿命、工作时间和修理时间均服从负指数分布. 利用马尔可夫过程理论、拉普拉斯变换, 给出了系统瞬态可用度、瞬态 故障频度、修理工繁忙的概率、修理设备更换的概率等可靠性指标的表达式. 进一步, 利用位相型分布的性质得到了系统可靠度、修理工的忙期分布函数的矩阵表达式. 在此基础上, 讨论了在不同的初始条件下系统相关指标随时间的变化情况, 并通过特殊情形的讨论数值验证了所得结果的正确性.

This paper considers the transient reliability measures of a $k$ out of $n$ warm standby system with repairman's multiple vacations and replaceable repair facility where the standby time, the operating time and the repair time of components all follow exponential distributions. Employing the Markov process theory and the Laplace transform tool, we deduce the analytical expressions of the transient system availability, the rate of occurrence of failures at time $t$, the probability that the repairman is busy with broken components and the probability that the repair facility is being replaced. Further, we derive the system reliability and the function of the busy period of the repairman with the probabilistic properties of the phase type distribution. Based on this, we discuss the time-dependent behavior of the system performance measures under different initial system states, and validate the correctness of our results through some special cases.