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修理设备可更换的k/n(G)表决可修系统
引用本文:吴文青,唐应辉,兰绍军.修理设备可更换的k/n(G)表决可修系统[J].数学学报,2016,59(6):799-820.
作者姓名:吴文青  唐应辉  兰绍军
作者单位:1. 西南科技大学理学院 绵阳 621000; 2. 四川师范大学 数学与软件科学学院 成都 610068; 3. 四川师范大学 数学与软件科学学院 成都 610068
基金项目:国家自然科学基金资助项目(71571127);国家自然科学基金青年项目(71301111);西南科技大学博士研究基金资助项目(15zx7141)
摘    要:研究了修理设备可更换的k/n(G)表决可修系统,其中修理设备在修理故障部件时可能发生失效.假定部件和修理设备的寿命服从负指数分布,故障部件的修理时间和修理设备的更换时间服从一般分布的条件下,利用马尔可夫更新过程理论和拉普拉斯变换(Laplace-Stieltjes变换),分别讨论了系统首次故障前的平均时间,可用度,故障频度及修理设备的不可用度和失效频度,获得了相关指标的递推表达式.在此基础上,给出了1/2(G)表决可修系统和(n-1)/n(G)表决可修系统相关可靠性指标的表达式.

关 键 词:k/n(G)表决可修系统  修理设备可更换  马尔可夫更新过程理论  可靠性指标

Analysis of k/n(G) Repairable System with Replaceable Repair Facility
Wen Qing WU,Ying Hui TANG,Shao Jun LAN.Analysis of k/n(G) Repairable System with Replaceable Repair Facility[J].Acta Mathematica Sinica,2016,59(6):799-820.
Authors:Wen Qing WU  Ying Hui TANG  Shao Jun LAN
Institution:1. School of Science, Southwest University of Science and Technology, Mianyang 621000, P. R. China; 2. School of Mathematics & Software Science, Sichuan Normal University, Chengdu 610068, P. R. China; 3. School of Mathematics & Software Science, Sichuan Normal University, Chengdu 610068, P. R. China
Abstract:This paper considers a k/n(G) repairable system with replaceable repair facility where the repair facility may fail during the repair period. Assume that the lifetime of each component and the work time of the repair facility are exponentially distributed random variables, while the repair time of broken component and the replacement time of the repair facility follow general distributions. By using the Markov renewal process theory and the Laplace (Laplace-Stieltjes) transform, the mean time to first failure, the availability and the rate of occurrence of failures of the system, the probability that the repair facility is being replaced and the rate of occurrence of failures of the repair facility are discussed. Further more, the recursive expressions of these reliability measures are obtained. Finally, two special cases 1/2(G) repairable system and (n-1)/n(G) repairable system are derived.
Keywords:k/n(G) repairable system  replaceable repair facility  Markov renewal process theory  reliability measures  
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