修理设备可更换的k/n(G)表决可修系统
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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.
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.
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.
引文
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[16]Tang Y.H.,Revisiting the model of servicing machines with repairable service facility-a new analyzing idea and some new results,Acta Mathematicae Applicatae Sinica,2010,26(4):557-566.
[17]Wu W.Q.,Tang Y.H.,Transient analysis of a fc-out-of-n:G system with N-policy,repairmen's multiple vacations,and redundant dependency,Discrete Dynamics in Nature and Society,2015,2015:1-13.
[18]Wu W.Q.,Tang Y.H.,Yu M.M.,et al.,Reliability analysis of a fc-out-of-n:G repairable system with single vacation,Applied Mathematical Modelling,2014,38(24):6075-6097.
[19]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.
[20]Yang W.,Gu J.H.,Reliability analysis for(n-l)/n(G)system(in Chinese),Mathematical Theory and Applicationgs,2006,27(2):71-73.
[21]Yu M.M.,Tang Y.H.,Fu Y.H.,et al.,A deteriorating repairable system with stochastic lead time and replaceable facility,Computer&Industrial Engineering,2012,62(2):609-615.
[22]Yuan L.,Reliability analysis for a fc-out-of-n:G system with redundant dependency and repairmen having multiple vacations,Applied Mathematics and Computation,2012,218(24):11959-11969.
[23]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.
[2]Birnbaum Z.W.,Esary J.D.,Saunders S.D.,Multi-component systems and structures and their reliability,Technometrics,1961,3(1):55-77.
[3]Cao J.H.,The model of servicing machines with repairable service facility(in Chinese),Journal of Mathematical Research and Exposition,1985,5(4):89-96.
[4]Cao J.H.,Cheng K.,Mathematical Theory of Reliability(Revised)(in Chinese),Higher Education Press,Beijing,2006.
[5]Cao J.H.,Wu Y.H.,Reliability analysis of a multistate system with a replaceable repair facility,Acta Mathematicae and Applicatae Sinica,1988,4(2):113-121.
[6]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.
[7]Chen T.,Li F.,Di P.,The reliability analysis of k-out-of-n system based on phase-type distribution(in Chinese),System Engineering-Theory&Practice,2015,35(1):260-266.
[8]Kang H.G.,Kim H.E.,Unavailability and spurious operation probability of fc-out-of-n reactor protection systems in consideration of CCF,Annals of Nuclear Energy,2012,94(2):102-108.
[9]Khatab A.,Nahas N.,Nourelfath M.,Availability of K-out-of-iV:G systems with non-identical components subject to repair priorities,Reliability Engineering and System Safety,2009,94(2):142-151.
[10]Kuo W.,Zuo M.J.,Optimal Reliability Modelling:Principles and Applications,John Wiley&Sons,New York,2003.
[11]Li X.H.,Zuo M.J.,Yam C.M.R.,Reliability analysis of a repairable fc-out-of-n system with some components being suspended when the system is down,Reliability Engineering and System Safety,2006,91(3):305-310.
[12]Mista K.B.,Handbook of Performability Engineering,Springer,London,2008.
[13]Moghaddas R.,Zuo M.J.,Wang W.B.,Availability of a general fc-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth-death process,Reliability Engineering and System Safety,2011,94(6):489-496.
[14]Neuts M.F.,Matrix-Geometric Solutions in Stochastic Models:An Algorithmic Approach,The Johns Hopkins University Press,Baltimore,1981.
[15]Ruiz-Castro J.E.,Li Q.L.,Algorithm for a general 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):97-111.
[16]Tang Y.H.,Revisiting the model of servicing machines with repairable service facility-a new analyzing idea and some new results,Acta Mathematicae Applicatae Sinica,2010,26(4):557-566.
[17]Wu W.Q.,Tang Y.H.,Transient analysis of a fc-out-of-n:G system with N-policy,repairmen's multiple vacations,and redundant dependency,Discrete Dynamics in Nature and Society,2015,2015:1-13.
[18]Wu W.Q.,Tang Y.H.,Yu M.M.,et al.,Reliability analysis of a fc-out-of-n:G repairable system with single vacation,Applied Mathematical Modelling,2014,38(24):6075-6097.
[19]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.
[20]Yang W.,Gu J.H.,Reliability analysis for(n-l)/n(G)system(in Chinese),Mathematical Theory and Applicationgs,2006,27(2):71-73.
[21]Yu M.M.,Tang Y.H.,Fu Y.H.,et al.,A deteriorating repairable system with stochastic lead time and replaceable facility,Computer&Industrial Engineering,2012,62(2):609-615.
[22]Yuan L.,Reliability analysis for a fc-out-of-n:G system with redundant dependency and repairmen having multiple vacations,Applied Mathematics and Computation,2012,218(24):11959-11969.
[23]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.