修理设备和开关不完全可靠的温贮备可修系统的可靠性
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摘要
最近,KUO和KE[Reliability Engineering and System Safety. 2016,145:74-82,参考文献[11]在假定部件故障后的修理时间以及修理设备故障后的修理时间均为一般分布的情形下,运用补充变量技术分别推导出三种可修系统模型的稳态可用度。然而作者并没有研究系统的瞬时可用度,本文在文献[11]的基础上,运用补充变量法推导出文献[11]中模型一的瞬时可用度的表达式。最后,用一个数值算例对所得结果进行了模拟实现。
Recently,KUO and KE[Reliability Engineering and System Safety. 2016,145: 74-82,see reference[11]assume that the repair time of the failure component and that of the failure server are general distribution,and the steady state availability of the three repairable systems are obtained by using supplementary variable method respectively. However,the instantaneous availability is not investigated in reference[11]. In this paper,the instantaneous availability of the model 1 is obtained by using supplementary variable method. Finally,a numerical example is given to illustrate these results obtained in the paper.
Recently,KUO and KE[Reliability Engineering and System Safety. 2016,145: 74-82,see reference[11]assume that the repair time of the failure component and that of the failure server are general distribution,and the steady state availability of the three repairable systems are obtained by using supplementary variable method respectively. However,the instantaneous availability is not investigated in reference[11]. In this paper,the instantaneous availability of the model 1 is obtained by using supplementary variable method. Finally,a numerical example is given to illustrate these results obtained in the paper.
引文
[1]曹晋华,程侃.可靠性数学引论[N].北京:科学出版社,2006:182-200.
[2] Colquhoun D,Hawks A G. On the stochastic properties of bursts of single ion channel opening and of clusters of bursts[J]. Philosophical Transactions of Royal Society B,1982,300,1-59.
[3] Cui L R,Li H J,Li J L. Markov repairable systems with history dependent up and down states[J]. Stochastic Models,2007,23(4):665-681.
[4] Wang L Y,Cui L R. Aggregated semi-markov repairable systems with history dependent up and down states[J].Mathematical and Computer Modeling,2011,53(5):883-895.
[5] Cui L R,Du S J,Liu B L. Multi-point and multi-interval availabilities[J]. IEEE Transactions on Reliability,2013,62(4):811-820.
[6] Neuts M F. Matrix-geometric solution in stochastic models-an algorithmic approach[M]. Baltimore:Johns Hopkins University Press,1981.
[7]温艳清,刘宝亮,罗芳,孟献青.可忽略部分维修时间且工作时间服从PH分布的单部件可修系统的可靠性[J].山东大学学报(理学版),2013,48(9):46-50.
[8] Liu B L,Cui L R,Wen Y Q,Shen J Y. A cold standby repairable system with working vacations and vacation interruption following markovian arrival process[J]. Reliability Engineering and System Safety,2015,142:1-8.
[9] Yuan L,Xu J. A deteriorating system with its repairman having multiple vacations[J]. Applied Mathematics and Computation,2011,217(10):4980-4989.
[10]刘宝亮,温艳清.修理工有多重休假的退化系统的可靠性[J].山东大学学报(理学版),2014,49(5):45-49.
[11] Kuo C C,Ke J C. Comparative analysis of standby systems with unreliable server and switching failure[J].Reliability Engineering and System Safety,2016,145:74-82.
[2] Colquhoun D,Hawks A G. On the stochastic properties of bursts of single ion channel opening and of clusters of bursts[J]. Philosophical Transactions of Royal Society B,1982,300,1-59.
[3] Cui L R,Li H J,Li J L. Markov repairable systems with history dependent up and down states[J]. Stochastic Models,2007,23(4):665-681.
[4] Wang L Y,Cui L R. Aggregated semi-markov repairable systems with history dependent up and down states[J].Mathematical and Computer Modeling,2011,53(5):883-895.
[5] Cui L R,Du S J,Liu B L. Multi-point and multi-interval availabilities[J]. IEEE Transactions on Reliability,2013,62(4):811-820.
[6] Neuts M F. Matrix-geometric solution in stochastic models-an algorithmic approach[M]. Baltimore:Johns Hopkins University Press,1981.
[7]温艳清,刘宝亮,罗芳,孟献青.可忽略部分维修时间且工作时间服从PH分布的单部件可修系统的可靠性[J].山东大学学报(理学版),2013,48(9):46-50.
[8] Liu B L,Cui L R,Wen Y Q,Shen J Y. A cold standby repairable system with working vacations and vacation interruption following markovian arrival process[J]. Reliability Engineering and System Safety,2015,142:1-8.
[9] Yuan L,Xu J. A deteriorating system with its repairman having multiple vacations[J]. Applied Mathematics and Computation,2011,217(10):4980-4989.
[10]刘宝亮,温艳清.修理工有多重休假的退化系统的可靠性[J].山东大学学报(理学版),2014,49(5):45-49.
[11] Kuo C C,Ke J C. Comparative analysis of standby systems with unreliable server and switching failure[J].Reliability Engineering and System Safety,2016,145:74-82.