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专职修理工多重休假且修理设备可更换的k/n(G)表决系统研究

张元元,吴文青   

  1. 西南科技大学
  • 收稿日期:2017-11-15 修回日期:2018-03-22 发布日期:2019-03-05
  • 通讯作者: 吴文青

Analysis of a k/n(G) system with expert repairman's multiple vacations and replaceable repair facility

  • Received:2017-11-15 Revised:2018-03-22 Published:2019-03-05
  • Contact: Wen-Qing WU

摘要: 本文讨论了专职修理工多重休假, 修理设备可发生失效且可更换的k/n(G)表决可修系统. 当系统中没有故障部件时, 专职修理工立即开始一次休假, 在此期间, 若有工作部件发生故障, 则立即指派普通修理工修理故障部件, 一直持续到系统中无故障部件或专职修理工休假回来. 利用马尔可夫过程理论和矩阵解法, 给出了系统瞬态和稳态下的可用度和故障频度、可靠度、系统首次故障前的平均时间、修理设备处于更换状态的概率等指标的表达式. 在此基础上, 基于不同的初始条件研究了相关指标随时间的变化情况. 最后, 特殊情形的讨论数值验证了所得结果的正确性.

关键词: k/n(G)表决系统, 专职修理工, 多重休假策略, 修理设备可更换, 可靠性指标

Abstract: This paper studies a repairable k/n(G) system with expert repairman's multiple vacations and replaceable repair facility. The expert repairman leaves for a vacation when there is no broken component. Once an operating component breaks down during his vacation period, it is repaired immediately by an ordinary repairman. The ordinary repairman becomes inactivated when there is no broken component or the expert returns from his vacation. By using the Markov process theory and the matrix solution method, we obtain the transient and the stationary of the system availability and the rate of occurrence of failures, the system reliability, the mean time to system failure, and the probability that the repair facility is being replaced. Further, we discuss the time-dependent behavior of the system reliability measures under different initial system states. Finally, special cases of the system is presented to show the correctness of our results.

Key words: k/n(G) system, expert repairman, multiple vacation policy, replaceable repair facility, reliability measures