修理设备可修修理延迟的N个部件串联系统的随机性状及可靠性分析
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摘要
考虑N(N≥2)个同型部件串联可修系统的随机性状及修理设备的可靠性.假设修理设备在修理失效部件的过程中可能失效,失效后的修理设备需要立即修理,部件失效后需要一段随机的延迟修理时间.进一步假定系统失效后好的部件可能劣化.利用马尔科夫更新过程工具和Takács的方法,研究系统的随机性状并利用随机性状研究结果得到该系统修理设备在时刻t的失效概率以及修理设备在(O,t)内的故障次数和故障频度以及一些有意义的推论.
This paper considers the stochastic behavior and the reliability of(N≥2)-unit series system. The repair facility is assumed to be repairable when it is down during repairing the failed component and all components are assumed as the same units. While a failed component needs to be repaired, there is often a stochastic delay time. Suppose that the remaining components which have been not failed may degenerate when the system is down. By the tool of Markov renewal processes and Takacs' methods, some stochastic behaviors of this system are obtained. Furthermore,the failure probability at time t and the failure frequency during the interval(0, t] of the repair facility and some corollaries are given.
This paper considers the stochastic behavior and the reliability of(N≥2)-unit series system. The repair facility is assumed to be repairable when it is down during repairing the failed component and all components are assumed as the same units. While a failed component needs to be repaired, there is often a stochastic delay time. Suppose that the remaining components which have been not failed may degenerate when the system is down. By the tool of Markov renewal processes and Takacs' methods, some stochastic behaviors of this system are obtained. Furthermore,the failure probability at time t and the failure frequency during the interval(0, t] of the repair facility and some corollaries are given.
引文
[1]曹晋华,程侃.可靠性数学引论.北京:科学出版社,1986.(Cao J H,Cheng K.Introduction to Reliability Mathematical Theory.Beijing:Science Press,1986.)
[2]曹晋华.修理设备可更换的Gnedenko系统可靠性分析.应用概率统计,1989,3:265-275.(Cao J H.Reliability analysis of Gnedenko system with a repair facility subject to failure and replacement.Chinese Journal of Applied Probability and Statistics,1989,3:265-275.)
[3]刘仁彬,唐应辉,骆川义.修理设备可更换且有修理延迟的N部件串联系统分析.数学的实践与认识,2007,1:49-54.(Liu R B,Tang Y H,Luo C Y.Reliability analysis of N-unit series system with a replaceable facility and delay repair.Mathematics in Practice and Theory,2007,1:49-54.)
[4]Takács L.Introduction to the Theory of Queues.Oxford:Oxford University Press,1962.
[5]曹晋华.服务设备可修的机器服务模型分析.数学研究与评论,1985,4:89-96.(Cao J H.Analysis of machine service model with repairable service equipment.Journal of Mathematical Research and Exposition,1985,4:89-96.)
[6]唐应辉,喻国建,李晓东.修理设备可更换且修理延迟的两同型部件并联可修系统.工程数学学报,2005,1:1-8.(Tang Y H,Yu G J,Li X D.Analysis of machine service model with repairable service equipment.Chinese Journal of Engineering Mathematics,2005,1:1-8.)
[7]曹晋华,程侃.服务台可修的M/G/1排队系统分析.应用数学学报,1982,2:118-127.(Cao J H,Cheng K.Analysis of M/G/1 queueing system with repairable service station.Acta Mathematicae Applicatae Sinica,1982,2:118-127.)
[8]Cinlar E.Introduction to Stochastic Processes.Englewood Cliffs.New Jersey:Prentice-Hall,Inc,1975.
[2]曹晋华.修理设备可更换的Gnedenko系统可靠性分析.应用概率统计,1989,3:265-275.(Cao J H.Reliability analysis of Gnedenko system with a repair facility subject to failure and replacement.Chinese Journal of Applied Probability and Statistics,1989,3:265-275.)
[3]刘仁彬,唐应辉,骆川义.修理设备可更换且有修理延迟的N部件串联系统分析.数学的实践与认识,2007,1:49-54.(Liu R B,Tang Y H,Luo C Y.Reliability analysis of N-unit series system with a replaceable facility and delay repair.Mathematics in Practice and Theory,2007,1:49-54.)
[4]Takács L.Introduction to the Theory of Queues.Oxford:Oxford University Press,1962.
[5]曹晋华.服务设备可修的机器服务模型分析.数学研究与评论,1985,4:89-96.(Cao J H.Analysis of machine service model with repairable service equipment.Journal of Mathematical Research and Exposition,1985,4:89-96.)
[6]唐应辉,喻国建,李晓东.修理设备可更换且修理延迟的两同型部件并联可修系统.工程数学学报,2005,1:1-8.(Tang Y H,Yu G J,Li X D.Analysis of machine service model with repairable service equipment.Chinese Journal of Engineering Mathematics,2005,1:1-8.)
[7]曹晋华,程侃.服务台可修的M/G/1排队系统分析.应用数学学报,1982,2:118-127.(Cao J H,Cheng K.Analysis of M/G/1 queueing system with repairable service station.Acta Mathematicae Applicatae Sinica,1982,2:118-127.)
[8]Cinlar E.Introduction to Stochastic Processes.Englewood Cliffs.New Jersey:Prentice-Hall,Inc,1975.