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

doi:10.15960/j.cnki.issn.1007-6093.2019.04.010

运筹学学报 ›› 2019, Vol. 23 ›› Issue (4): 111-123.doi: 10.15960/j.cnki.issn.1007-6093.2019.04.010

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^1,2, 吴文青^1,2,*

1. 西南科技大学理学院, 四川绵阳 621010;
2. 可视化计算与虚拟现实四川省重点实验室, 成都 610068

收稿日期:2017-11-15 发布日期:2019-12-04
通讯作者: 吴文青 E-mail:wwqing0704@swust.edu.cn
基金资助:
西南科技大学龙山学术人才科研支持计划（No.17LZXY20），可视化计算与虚拟现实四川省重点实验室基金（No.SCVCVR2018.10VS），国家自然科学基金（No.71571127）

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

ZHANG Yuanyuan^1,2, WU Wenqing^1,2,*

1. School of Science, Southwest University of Science and Technology, Mianyang 621010, Sichuan, China;
2. Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610068, China

Received:2017-11-15 Published:2019-12-04

摘要/Abstract

摘要： 讨论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 these reliability measures under different initial states. Finally, special cases of the system are presented to show the correctness of our results.

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

中图分类号:

O213.2

张元元, 吴文青. 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[J]. 运筹学学报, 2019, 23(4): 111-123.

ZHANG Yuanyuan, WU Wenqing. Analysis of a k/n(G) system with expert repairman's multiple vacations and replaceable repair facility[J]. Operations Research Transactions, 2019, 23(4): 111-123.

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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

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

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