修理工多重休假且修理设备可更换的k/n(G)表决可修系统研究

吴文青, 唐应辉, 姜颖

系统工程理论与实践 ›› 2013, Vol. 33 ›› Issue (10) : 2604-2614.

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系统工程理论与实践 ›› 2013, Vol. 33 ›› Issue (10) : 2604-2614. DOI: 10.12011/1000-6788(2013)10-2604
论文

修理工多重休假且修理设备可更换的k/n(G)表决可修系统研究

    吴文青1, 唐应辉1, 姜颖1,2
作者信息 +

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

    WU Wen-qing1, TANG Ying-hui1, JIANG Ying1,2
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文章历史 +

摘要

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.

Abstract

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 expressions 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.

关键词

k/n(G)表决系统 / 多重休假 / 修理设备可更换 / 可靠性指标 / 排队指标

Key words

k-out-of-n:G system / multiple vacations / replaceable repair facility / reliability index / queueing index

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吴文青 , 唐应辉 , 姜颖. 修理工多重休假且修理设备可更换的k/n(G)表决可修系统研究. 系统工程理论与实践, 2013, 33(10): 2604-2614 https://doi.org/10.12011/1000-6788(2013)10-2604
WU Wen-qing , TANG Ying-hui , JIANG Ying. Study on a k-out-of-n:G repairable system with multiple vacations and one replaceable repair facility. Systems Engineering - Theory & Practice, 2013, 33(10): 2604-2614 https://doi.org/10.12011/1000-6788(2013)10-2604
中图分类号： O213.2    O226   

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基金

国家自然科学基金(71171138, 70871084);教育部高校博士点专项基金(200806360001)
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