修理工带休假的n部件冷贮备可修系统

对由1个修理工和n个部件组成的冷贮备可修系统的可靠性进行了研究,当系统中没有故障部件时,修理工可以进行多重休假,休假时间是一个随机变量;在修理工休假期间,如果系统中在线工作的部件出现了故障,则其中一个冷贮备部件立即代替故障部件成为在线工作部件,故障部件必须等待修理工从休假返回才能得到修理。假定部件的工作时间、部件故障后的修理时间以及修理工的休假时间均为位相型(PH)分布。通过运用Kronecker算子和马尔可夫过程理论,分别推导出系统在瞬态和稳态情况下的几个可靠性指标:可靠度、可用度、故障频度以及修理工忙的概率。通过数值算例对所得结论进行了验证。

Cold standby n-component repairable system with repairman vacation

The reliability for a cold standby n-component repairable system with a repairman having multiple vacations is studied. If all of units are in normal state, the repairman may take his vacations, and the vacation time is a random variable. During the repairman's vacation, if a unit online fails to work, one of cold standby components becomes the component online immediately the failure unit will not be repaired until the repairman comes back from his vacation. The operational time of the unit online, the repair time and the vacation time of repairman are governed by different phase-type (PH) distributions, respectively. The system is studied in a transient and stationary regime. The reliability, availability, rate of occurrence of failures and busy probability of repairman are derived by Kronecker operator and Markov process theory. A numerical example is given to illustrate the results obtained.