具有单重休假和修复不如新的两部件温贮备系统

刘海涛; 孟宪云

doi:10.3724/SP.J.1004.2012.00639

具有单重休假和修复不如新的两部件温贮备系统

doi: 10.3724/SP.J.1004.2012.00639

刘海涛,
孟宪云^,

1.
燕山大学理学院秦皇岛 066004

详细信息

通讯作者:
孟宪云燕山大学理学院教授. 主要研究方向为可靠性理论及应用. E-mail: mengxianyun2008@126.com

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出版历程
- 收稿日期: 2011-03-10
- 修回日期: 2011-11-10
- 刊出日期: 2012-04-20

A Warm Standby System with Repair of Non-new and Repairman Vacation

LIU Hai-Tao,
MENG Xian-Yun^,

1.
College of Sciences, Yanshan University, Qinhuangdao 066004

摘要

摘要: 研究了修理工单重休假且由两个不同型部件和一个修理工组成的可修型温贮备系统. 系统考虑了在工作故障和贮备故障都不能 “修复如新”, 部件 1 是修复非新而部件 2 修复如新的条件下, 假设部件的工作寿命、贮备寿命、故障后的修理时间和贮备故障后的修理时间均服从不同的指数分布, 修理工休假服从一般连续型分布. 运用几何过程理论、补充变量法、拉普拉斯变换及拉普拉斯--司梯阶变换, 得到了系统的可用度、可靠度和系统首次故障前平均时间等可靠性指标. 最后, 通过数值模拟验证了结果的有效性.
- 几何过程 /
- 补充变量法 /
- 休假 /
- 马尔科夫过程 /
- 拉普拉斯变换
Abstract: A repairable warm standby system composed of two different components and one repairman who has vacation is studied. The system considers the work fault and standby fault is not “as good as new”, and the repair of component 1 is not as good as new and repair of component 2 is as good as new. Assume that the working time, the standby time, the repair time after fault and the repair time after standby fault of two components are subject to different exponential distributions, and that the repairman vacation time obeys the general distribution. The system's availability, reliability, the system average working time to first failure and other reliability indices are obtained by using the geometric process theory, the supplementary variable method, Laplace transform and Laplace-Stieltjes transform. Finally, a numerical example is given to simulate the effective of the results.
- Geometric process /
- supplementary variable /
- vacation /
- Markov process /
- Laplace transform

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参考文献(1)

[1]

Cao Jin-Hua, Cheng Kan. Introduction to Mathematical Theory of Reliability. Beijing: Science Press, 1986(曹晋华, 程侃. 可靠性数学引论. 北京: 科学出版社, 1986)[2] Meng Xian-Yun, Liu Yan, Chen Guang-Juan, Liu Le-Chun, Yin Rui-Ling, Yuan Li. Reliability analysis of warm standby repairable system of two components with continuous lifetime switch and priority. Journal of Yanshan University, 2006, 30(1): 51-56(孟宪云, 刘艳, 陈广娟, 刘乐春, 阴瑞玲, 袁丽. 有优先权且有两个不同修理工的两部件温贮备可修系统的可靠性分析. 燕山大学学报, 2006, 30(1): 51-56)[3] Tang Ying-Hui, Liu Xiao-Yun. Reliability analysis of one unit repairable system with repairman vacation. Acta Automatica Sinica, 2004, 30(3): 466-470(唐应辉, 刘晓云. 修理工带休假的单部件可修系统的可靠性分析. 自动化学报, 2004, 30(3): 466-470)[4] Yuan L, Meng X Y. Reliability analysis of a warm standby repairable system with priority in use. Applied Mathematical Modelling, 2011, 35(9): 4295-4303[5] Lam Y. Geometric process and replacement problem. Acta Mathematicae Applicatae Sinica, 1988, 4(4): 366-377[6] Liu Hai-Tao, Meng Xian-Yun, Li Fang, Fu Qin-Hui, Zhang Jian-Long. A geometric process model for two different components of warm standby system. Systems Engineering, 2010, 28(9): 103-107(刘海涛, 孟宪云, 李芳, 付钦慧, 张建龙. 两个不同型部件温贮备系统的几何过程模型. 系统工程, 2010, 28(9): 103-107)[7] Meng Xian-Yun, Liu Hai-Tao, Li Fang, Zhang Jian-Long, Fu Qin-Hui. Geometric process model for two type components in cold standby system. Journal of Liaoning Technical University (Natural Science), 2011, 30(1): 146-149(孟宪云, 刘海涛, 李芳, 张建龙, 付钦慧. 两个不同型部件冷贮备系统的几何过程模型. 辽宁工程技术大学学报 (自然科学版), 2011, 30(1): 146-149)[8] Cheng Zhi-Jun, Guo Bo. Optimization of inspection and maintenance policy for deteriorating system with semi-Markov decision. Acta Automatica Sinica, 2007, 33(10): 1101-1104(程志军, 郭波. 基于半 Markov 决策过程的劣化系统检测与维修优化模型. 自动化学报, 2007, 33(10): 1101-1104)[9] Su Bao-He, Lin Fu-Yong, Zhang Wen-Guo, Liu Bao-You. Research on the inspection polices of 2-failure-model systems. Acta Automatica Sinica, 2003, 29(4): 544-549[10] Su Bao-He. Reliability indices and optimal checking policies for a repairable system. Acta Automatica Sinica, 2002, 28(1): 116-119(苏保河. 一类可修系统的可靠性指标和最优检测策略. 自动化学报, 2002, 28(1): 116-119)[11] Liu Bao-You, Su Bao-He. Diagnostic repairable system of special state and special repair. Acta Automatica Sinica, 2002, 28(1): 97-106, 119(刘宝友, 苏保河. 特殊状态需要特殊修理的诊断可修系统. 自动化学报, 2002, 28(1): 97-106, 119)[12] Yuan L, Xu J. A deteriorating system with its repairman having multiple vacations. Applied Mathematics and Computation, 2011, 217(10): 4980-4989[13] Yuan L, Xu J. An optimal replacement policy for a repairable system based on its repairman having vacations. Reliability Engineering and System Safety, 2011, 96(7): 868 -875

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