两水平修理策略的k/n(G)表决系统可靠性分析
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摘要
研究了具有两水平修理策略和两类修理工的表决可修系统,其中部件的工作时间和修理时间均服从负指数分布.使用马尔可夫分析方法和马氏链吸收时间理论,讨论了系统可用度、故障频度、首次故障前的平均时间等指标.在此基础上,分析了不同条件下系统相关指标随系统参数变化的情况.最后,通过蒙特卡罗仿真和特殊情形的数值结果验证了所得表达式的正确性.
This paper investigates a repairable system with bi-level repair strategy and two types of repairmen,in which the working times and repair times of components follow exponential distributions. Employing the Markov analysis method and the theory of the absorption time of a Markov chain, this paper discusses the system availability, the rate of occurrence of failures of the system, the mean time prior to failure of the system and some other system performance measures. Further, this paper also analyzes the influence of system parameters on system reliability measures. Finally, Monte Carlo simulation and special cases are provided to show the correctness of the theoretical results.
This paper investigates a repairable system with bi-level repair strategy and two types of repairmen,in which the working times and repair times of components follow exponential distributions. Employing the Markov analysis method and the theory of the absorption time of a Markov chain, this paper discusses the system availability, the rate of occurrence of failures of the system, the mean time prior to failure of the system and some other system performance measures. Further, this paper also analyzes the influence of system parameters on system reliability measures. Finally, Monte Carlo simulation and special cases are provided to show the correctness of the theoretical results.
引文
[1]Kuo W,Zuo M J.Optimal Reliability Modelling:Principles and Applications.New York:John Wiley&Sons,2003.
[2]曹晋华,程侃.可靠性数学引论.北京:高等教育出版社,2006.Cao J H,Cheng K.Mathematical Theory of Reliability.Beijing:Higher Education Press,2006.(in Chinese)
[3]陈童,黄卓,谭林,等.考虑库存损耗的单部件系统可修备件需求模型.系统工程学报,2012,27(2):270-278.Chen T,Huang Z,Tan L,et al.Repairable spare parts demand model of single unit system with perishable inventory.Journal of Systems Engineering,2012,27(2):270-278.(in Chinese)
[4]刘仁彬,邓朝晖,刘锋.一类多级适应性休假的串联可修系统分析.系统工程学报,2014,29(1):126-134.Liu R B,Deng Z H,Liu F.Analysis of a series repairable system with multiple adaptive vacations.Journal of Systems Engineering,2014,29(1):126-134.(in Chinese)
[5]刘仁彬.多级适应性休假的两部件系统及其优化应用.系统工程学报,2016,31(2):281-288.Liu R B.Two-unit system with multiple adaptive vacations and its optimization application.Journal of Systems Engineering,2016,31(2):281-288.(in Chinese)
[6]Chang G J,Cui L R,Hwang F R.Reliabilities for(n,f,k)system.Statistics&Probability Letters,1999,43(3):237-242.
[7]李春洋,陈循,易晓山,等.基于马尔可夫过程的k/n(G)系统共因失效分析.系统工程与电子技术,2009,31(11):2789-2792.Li C Y,Chen X,Yi X S,et al.Analysis of k-out-of-n:G systems subject to common cause failures based on Markov process.System Engineering and Electronics,2009,31(11):2789-2792.(in Chinese)
[8]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.Wu W Q,Tang Y H,Jiang Y.Study on a k-out-of-n:G repairable system with multiple vacations and one replaceable repair facility.System Engineering:Theory&Practice,2013,33(10):2604-2614.(in Chinese)
[9]陈童,黎放,狄鹏.基于PH分布的n中取k系统可靠性模型研究.系统工程理论与实践,2015,35(1):260-266.Cheng T,Li F,Di P.The reliability analysis of k-out-of-n system based on phase-type distribution.System Engineering:Theory&Practice,2015,35(1):260-266.(in Chinese)
[10]Zhang Y L,Wu S M.Reliability analysis for a k/n(F)system with repairable repair-equipment.Applied Mathematical Modelling,2009,33(7):3052-3067.
[11]Krishnamoorthy A,Ushakumari P V.k-out-of-n:G system with repair:The D-policy.Computers&Operations research,2001,28(10):973-981.
[12]Krishnamoorthy A,Rekha A.k-out-of-n system with repair:T-policy.The Korean Journal of Computational and Applied Mathematics,2001,8(1):199-212.
[13]Krishnamoorthy A,Ushakumari P V,Lakshmy B.k-out-of-n system with repair:The N-policy.Asia-Pacifc Journal of Operational Research,2002,19(1):47-61.
[14]Wu W Q,Tang Y H,Yu M M,et al.Computation and profit analysis of a k-out-of-n:G repairable system under N-policy with multiple vacations and one replaceable repair facility.RAIRO:Operations Research,2015,49(4):717-734.
[15]Li X H,Zuo M J,Yam C M R.Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down.Reliability Engineering and System Safety,2006,91(3):305-310.
[16]Chakravarthy S R,Gomez-Corral A.The influence of delivery times on repairable K-out-of-N systems with spares.Applied Mathematical Modelling,2009,33(5):2368-2387.
[17]Moghaddass R,Zuo M J,Qu J.Reliability and availability analysis of a repairable k-out-of-n:G system with R repairmen subject to shut-off rules.IEEE Transactions on Reliability,2011,60(3):658-666.
[18]Ruiz-Castro J E,Li Q L.Algorithm for a discrete k-out-of-n:G system subject to several types of failure with an indefinite number of repairpersons.European Journal of Operational Research,2011,211(1):91-111.
[19]Eryilmaz S,Xie M.Dynamic modeling of general three-state k-out-of-n:G systems:Permanent-based computational results.Journal of Computational and Applied Mathematics,2014,272(15):97-106.
[20]付永红,余玅妙,唐应辉,等.两水平维修策略下的M/(Mr,Ms)/1/N/N机器维修模型稳态概率算法与性能分析.山东大学学报(自然科学版),2009,44(4):72-78.Fu Y H,Yu M M,Tang Y H,et al.Steady-state probability algorithm and performance evaluation for M/(Mr,Ms)/1/N/Nmachine repair model under bi-level repair facility.Journal of Shangdong University(Natural Science Edition),2009,44(4):72-78.(in Chinese)
[21]Tian N S,Zhang Z G.Vacation Queueing Models:Theory and Applications.New York:Springer-Verlag,2006.
[2]曹晋华,程侃.可靠性数学引论.北京:高等教育出版社,2006.Cao J H,Cheng K.Mathematical Theory of Reliability.Beijing:Higher Education Press,2006.(in Chinese)
[3]陈童,黄卓,谭林,等.考虑库存损耗的单部件系统可修备件需求模型.系统工程学报,2012,27(2):270-278.Chen T,Huang Z,Tan L,et al.Repairable spare parts demand model of single unit system with perishable inventory.Journal of Systems Engineering,2012,27(2):270-278.(in Chinese)
[4]刘仁彬,邓朝晖,刘锋.一类多级适应性休假的串联可修系统分析.系统工程学报,2014,29(1):126-134.Liu R B,Deng Z H,Liu F.Analysis of a series repairable system with multiple adaptive vacations.Journal of Systems Engineering,2014,29(1):126-134.(in Chinese)
[5]刘仁彬.多级适应性休假的两部件系统及其优化应用.系统工程学报,2016,31(2):281-288.Liu R B.Two-unit system with multiple adaptive vacations and its optimization application.Journal of Systems Engineering,2016,31(2):281-288.(in Chinese)
[6]Chang G J,Cui L R,Hwang F R.Reliabilities for(n,f,k)system.Statistics&Probability Letters,1999,43(3):237-242.
[7]李春洋,陈循,易晓山,等.基于马尔可夫过程的k/n(G)系统共因失效分析.系统工程与电子技术,2009,31(11):2789-2792.Li C Y,Chen X,Yi X S,et al.Analysis of k-out-of-n:G systems subject to common cause failures based on Markov process.System Engineering and Electronics,2009,31(11):2789-2792.(in Chinese)
[8]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.Wu W Q,Tang Y H,Jiang Y.Study on a k-out-of-n:G repairable system with multiple vacations and one replaceable repair facility.System Engineering:Theory&Practice,2013,33(10):2604-2614.(in Chinese)
[9]陈童,黎放,狄鹏.基于PH分布的n中取k系统可靠性模型研究.系统工程理论与实践,2015,35(1):260-266.Cheng T,Li F,Di P.The reliability analysis of k-out-of-n system based on phase-type distribution.System Engineering:Theory&Practice,2015,35(1):260-266.(in Chinese)
[10]Zhang Y L,Wu S M.Reliability analysis for a k/n(F)system with repairable repair-equipment.Applied Mathematical Modelling,2009,33(7):3052-3067.
[11]Krishnamoorthy A,Ushakumari P V.k-out-of-n:G system with repair:The D-policy.Computers&Operations research,2001,28(10):973-981.
[12]Krishnamoorthy A,Rekha A.k-out-of-n system with repair:T-policy.The Korean Journal of Computational and Applied Mathematics,2001,8(1):199-212.
[13]Krishnamoorthy A,Ushakumari P V,Lakshmy B.k-out-of-n system with repair:The N-policy.Asia-Pacifc Journal of Operational Research,2002,19(1):47-61.
[14]Wu W Q,Tang Y H,Yu M M,et al.Computation and profit analysis of a k-out-of-n:G repairable system under N-policy with multiple vacations and one replaceable repair facility.RAIRO:Operations Research,2015,49(4):717-734.
[15]Li X H,Zuo M J,Yam C M R.Reliability analysis of a repairable k-out-of-n system with some components being suspended when the system is down.Reliability Engineering and System Safety,2006,91(3):305-310.
[16]Chakravarthy S R,Gomez-Corral A.The influence of delivery times on repairable K-out-of-N systems with spares.Applied Mathematical Modelling,2009,33(5):2368-2387.
[17]Moghaddass R,Zuo M J,Qu J.Reliability and availability analysis of a repairable k-out-of-n:G system with R repairmen subject to shut-off rules.IEEE Transactions on Reliability,2011,60(3):658-666.
[18]Ruiz-Castro J E,Li Q L.Algorithm for a discrete k-out-of-n:G system subject to several types of failure with an indefinite number of repairpersons.European Journal of Operational Research,2011,211(1):91-111.
[19]Eryilmaz S,Xie M.Dynamic modeling of general three-state k-out-of-n:G systems:Permanent-based computational results.Journal of Computational and Applied Mathematics,2014,272(15):97-106.
[20]付永红,余玅妙,唐应辉,等.两水平维修策略下的M/(Mr,Ms)/1/N/N机器维修模型稳态概率算法与性能分析.山东大学学报(自然科学版),2009,44(4):72-78.Fu Y H,Yu M M,Tang Y H,et al.Steady-state probability algorithm and performance evaluation for M/(Mr,Ms)/1/N/Nmachine repair model under bi-level repair facility.Journal of Shangdong University(Natural Science Edition),2009,44(4):72-78.(in Chinese)
[21]Tian N S,Zhang Z G.Vacation Queueing Models:Theory and Applications.New York:Springer-Verlag,2006.