推广下的串联可修系统的可靠性分析
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摘要
可靠性系统的可靠性是可靠性研究中一个非常重要的内容,本文在已有的可修系统可靠性研究成果的基础之上,对一些特殊的串联可修系统进行了分析和讨论:
1)讨论了经典的n部件串联可修系统的可靠性。
2)进一步分析了部件不能够立即被修理的n部件串联系统的可靠性,即当系统出现故障时,修理工需要等待一段时间,才能进入修理状态,并且不同的部件,故障以后的等待修理时间服从不同的一般分布,本文主要利用更新过程理论,讨论了系统的可靠度,可用度,首次故障时间和(0,t]时间内的系统平均故障次数等可靠性指标。
3)讨论了修理工有兼职的n部件串联可修系统的可靠性。通过使用补充变量法,向量马尔可夫过程方法和拉普拉斯变换工具,讨论了系统的瞬时可用度和稳态可用度,以及在(0,t]时间内的系统平均故障次数和稳态故障频度,得到了系统的主要可靠性指标的拉普拉斯变换表达式,并进行了系统的效益分析,分析了何时应该鼓励修理工兼职,何时应限制兼职。
4)现实情形中,部件的故障可能有多种,本文最后一章姑且假设部件的故障只有两种类型,把它分为轻故障和重故障两种,从而使得串联部件的模型进一步完善。应用概率分析和补充变量法,求得了系统一些重要的可靠性指标。
Reliability of the reliability system is a very important element of reliability study. On the basis of the research of repairable reliability system, this paper attempts to analyze and discuss some special series of repairable systems.
1) Analysis on the classical series of repairable reliability of the system.
2) This paper further analyzes n Series reliability of the system components which can not be repaired immediately, that is the repairman can not repair immediately, and to wait for a period of time, This paper mainly uses this update process theory to discuss reliability indices such as the system reliability, availability, the first failure MTTFF time, the average time of the system fault frequency in the time of (0, t], etc.
3) This paper also discusses the part-time repairman with n components series repairable system reliability. Through the use of supplementary variables, methods of Markov process and vector Lap Lace Transform, this paper discusses the system instantaneous availability and steady availability, and (0, t] time in the system and the average number of faults fault steady frequency, and concludes that the main indicators of reliability is the Lap lace transform expression. This paper also discusses the effectiveness of the system.
4) In the course of the discussion above, we only hypothesize one component of the fault, but in real life, there are many component failures. In order to make up for the lack of discussion above, and to facilitate the discussion, let us assume that there are only two components of fault. It is divided into light and heavy ones. A series of components model will be further perfected, closer to reality, and also has more real value. Probability and supplementary variable are still the main method of analysis, by which we can obtain all the important reliability indicators in the system
1)讨论了经典的n部件串联可修系统的可靠性。
2)进一步分析了部件不能够立即被修理的n部件串联系统的可靠性,即当系统出现故障时,修理工需要等待一段时间,才能进入修理状态,并且不同的部件,故障以后的等待修理时间服从不同的一般分布,本文主要利用更新过程理论,讨论了系统的可靠度,可用度,首次故障时间和(0,t]时间内的系统平均故障次数等可靠性指标。
3)讨论了修理工有兼职的n部件串联可修系统的可靠性。通过使用补充变量法,向量马尔可夫过程方法和拉普拉斯变换工具,讨论了系统的瞬时可用度和稳态可用度,以及在(0,t]时间内的系统平均故障次数和稳态故障频度,得到了系统的主要可靠性指标的拉普拉斯变换表达式,并进行了系统的效益分析,分析了何时应该鼓励修理工兼职,何时应限制兼职。
4)现实情形中,部件的故障可能有多种,本文最后一章姑且假设部件的故障只有两种类型,把它分为轻故障和重故障两种,从而使得串联部件的模型进一步完善。应用概率分析和补充变量法,求得了系统一些重要的可靠性指标。
Reliability of the reliability system is a very important element of reliability study. On the basis of the research of repairable reliability system, this paper attempts to analyze and discuss some special series of repairable systems.
1) Analysis on the classical series of repairable reliability of the system.
2) This paper further analyzes n Series reliability of the system components which can not be repaired immediately, that is the repairman can not repair immediately, and to wait for a period of time, This paper mainly uses this update process theory to discuss reliability indices such as the system reliability, availability, the first failure MTTFF time, the average time of the system fault frequency in the time of (0, t], etc.
3) This paper also discusses the part-time repairman with n components series repairable system reliability. Through the use of supplementary variables, methods of Markov process and vector Lap Lace Transform, this paper discusses the system instantaneous availability and steady availability, and (0, t] time in the system and the average number of faults fault steady frequency, and concludes that the main indicators of reliability is the Lap lace transform expression. This paper also discusses the effectiveness of the system.
4) In the course of the discussion above, we only hypothesize one component of the fault, but in real life, there are many component failures. In order to make up for the lack of discussion above, and to facilitate the discussion, let us assume that there are only two components of fault. It is divided into light and heavy ones. A series of components model will be further perfected, closer to reality, and also has more real value. Probability and supplementary variable are still the main method of analysis, by which we can obtain all the important reliability indicators in the system
引文
[1]Markov A.A.Extension of the law of large numbers to dependent quantities in Russian.IZV.FIZ-Matem.Kazan Univ.(2~(nd)ser),1906(15):135-156
[2]侯振挺等.马尔可夫骨架过程—混杂系统模型.长沙:湖南科学技术出版社,2000
[3]侯振挺等.生灭过程.长沙:湖南科学技术出版社,2000
[4]Levy P.Semi—Markovian Processes.Proc:Ⅲ Intenat.Congr.Math.1954,416-426
[5]Davis M.H.A.a Piecewise—deterministic Markov process:a general class of non-diffusion stochastic models.J.R.Statist.Soc,B,1984(46):353-388
[6]Davis M.H.A.Markov models and optimization.London:Chapman and Hall,1993
[7]Hou Zhenting,Liu Zaiming,Zou Jiezhong.QNQL-Process:(H,Q)-process and their Application.Chinese Science Bulletin,1997,42(11):881-886
[8]Hou Zhenting,Liu Zaiming,Zou Jiezhong.Markov skeleton processes.Chinese Science Bulletin,1998,43(11):881-889
[9]侯振挺,郭先平.马尔可夫决策过程.长沙:湖南科学技术出版社,1997
[10]Hou Zhenting.Markov Skeleton Process and applications to queuing systems.Acta,Mathematic Application Sinica,English Series,2002,18(4):537-552
[11]Hou Zhenting,Yuan Chenggui,Zou Jiezhong et al.Transient distribution of the length of GI/G/n queuing systems.Stochastic Analysis and Applications,2003,21(3):567-592
[12]王益民.马尔可夫骨架过程在GI/G/n排队系统中的应用:[博士学位论文].长沙:中南大学,2002
[13]何宁卡.马尔可夫骨架过程的极限理论及其应用:[博士学位论文].长沙:中南大学,2004
[14]蒋放鸣.马尔可夫骨架过程及其应用:[博士学位论文].长沙:中南大学,2004
[15]戴清.马尔可夫骨架过程及其在Frac/G/1排队轮中的应用:[博士学位论文].长沙:中南大学,2004
[16]黄奇.马尔可夫骨架过程在可靠性理论中的应用:[博士学位论文].长沙:中南大学,2004
[17]Hou Zhenting,Liu Guoxing.Markov Skeleton Processes and their applications.Beijing:Science Press,2005
[18]Hou Zhenting,Liu Guoxing.Markov Skeleton Process and their applications.School of Manthematics,Central South University.March 2005
[19]Palm C.Arbetskraftens fordeling rid betjaning av automatckiner.Industritigen Norden,1947(75):75-80,90-94,119-123
[20]Lotka A.J.A contribution to the theory of self-renewing aggregates with special reference to industrial replacement.Ann.Math.Statist,1939(10):1-25
[21]Carnbell N.R.The replacement of perishable members of a continually operating system.J.Roy.Statist 1941(7):110-130
[22]Weibull W.A statistical theory of the strength of materials.Ing.Vetenskaos Akad.Handl.1939(152):1-45
[23]Gumbel E.J.Les vaeurs extremes des distributions statistiques.Annales de I'Institute Henri I' oincare,1935(4):115
[24]Epstein B.Application of the theory of extreme values in fracture problems.J.Amer.Statist Assoc.1948(43):403-412
[25]Barlow R.E.and Proschan F.S.Statistical theory of reliability and life testing,to begin with silver.Springer,MD,1981
[26]曹晋华,程侃.可靠性数学引论.北京:科学出版社,1986
[27]史定华.随机模型的密度演化方法.北京:科学出版社,1999
[28]程侃.寿命分布类与可靠性数学理论.北京:科学出版社,1999
[29]秦英孝.可靠性、维修性、保障性概论.北京:国防工业出版社,2002
[30]曹晋华,程侃.使用和修理有优先权的两部件冷贮备系统的可靠性分析.上海铁道学院学报,1981(4):31-45
[31]刘鸣,苏保河.修理工多重休假两部件冷贮备可修系统.石家庄铁道学院学报,1994,7(3):47-52
[32]唐应辉,刘燕.修理延迟的两个不同型部件冷贮备系统.电子科技大学学报,2004,33(3):331-333
[33]李伟,史定华.具有p_1优先使用权和p_2优先修理权的一半两部件冷贮备系统分析.数理统计与应用概率,1994,9(3):85-98
[34]徐光辉.随机服务系统.北京:科学出版社,1988
[35]周永卫.数学模型中的马尔可夫骨架过程方法:[硕士学位论文].长沙:中南大学,2005
[36]范贺花.马尔可夫骨架过程在数学模型中的应用:[硕士学位论文]. 长沙:中南大学,2005
[37]姜启源,谢金星,叶俊.数学模型.北京:高等教育出版社,2003
[38]唐应辉,刘晓云.一种新型的单部件可修系统.系统工程理论与实践,2003(7):106-109
[39]刘宝友.两不同部件冷贮备可修系统的可靠性分析.石家庄铁道学院学报,1994,7(4):44-50
[40]苏保河.冷贮备可修系统的一个模型及其经济分析.数学的实践与认识,1996,26(4):351-35
[41]周家良,王乃鹏.修理设备可更换的两部件并联可修系统的可靠性分析.工程数学学报,1994,11(4):73-80
[42]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
[43]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,2005,22(1):1-8
[44]吴清太,叶尔骅.开关寿命连续型二部件温贮备可修系统的可靠性分析.应用概率统计,2001,17(2):175-179
[45]科学出版社名词室编.新英汉数学词汇.北京:科学出版社,2002
[46]Zhang,H.et al,"Strong periodicity of monotone transition functions,"Statistic & Probability Letters,55,pp.63-69,2001.
[47]K.Thiruvengdan,Queueing with breakdown,Opns.Res.11,62-71(1963).
[48]Zhang,H.et al,"Strong periodicity of monotone transition functions,"Statistic & Probability Letters,55,pp.63-69,2001.
[49]Fort,G.and Moulines,E.Polynomial ergodicity of Markov transition kernels.Stoch.Proc.Appl.103,57-99(2003)
[50]Meyn,S.P.and Tweedier,R.L.Computable bounds for geometric convergence rates of Marko chains.Ann.Appl.Prob.4,981-1011(1994)
[51]Soulier,PH.,Douc,R.,Fort,G.,and Moulines,E.Practical drift conditions for subgeometricrates of convergence.Ann.Appl.Prob.14(3),1353-1377(2004)
[52]Jarner,S.and Roberts,G.Polynomial convergence rates of Markov chains.Ann.Appl.Prob.12,224-247(2001)
[53]Gut,A.On the moments of some first passage times for sums of dependent random variables.Stoch.Proc.Appl.2,115-126(1974)
[54]Zhang,H.et al,"Strong periodicity of monotone transition functions,"Statistic & Probability Letters,55,pp.63-69,2001.
[55]R.E.Barlow and L.C.Hunter,Reliability analysis of a one-unit system.Opns.Res.19,200-208(1961).
[56]Tang Y H.Some new results on one unit repairable system[J].Microelectronics & Reliability,1996;(36):199-202
[57]K.Thiruvengdan,Queueing with breakdown,Opns.Res.11,62-71(1963).
[58]Y.H.Tang,Some reliability problems arising in GI/G/1 queueing system with repairable service station,Microelectron.Reliab.35,707-712(1995).
[59]R.E.Barlow and L.C.Hunter,Reliability analysis of a one-unit system.Opns.Res.19,200-208(1961).
[60]Hou,Z.T.and Liu,Y.Y.Explicit criteria for several types of ergodicity of the embeddedM/G/1 and GI/M/n queues.J.App.Prob.41,778-790(2004)
[61]逯昭义,环形LAN多令牌存取方式的排队模型.通信学报,1991,12(5):15-21.
[62]R.E.Barlow and L.C.Hunter,Reliability analysis of a one-unit system.Opns.Res.19,200-208(1961).
[63]K.Thiruvengdan,Queueing with breakdown,Opns.Res.11,62-71(1963).
[2]侯振挺等.马尔可夫骨架过程—混杂系统模型.长沙:湖南科学技术出版社,2000
[3]侯振挺等.生灭过程.长沙:湖南科学技术出版社,2000
[4]Levy P.Semi—Markovian Processes.Proc:Ⅲ Intenat.Congr.Math.1954,416-426
[5]Davis M.H.A.a Piecewise—deterministic Markov process:a general class of non-diffusion stochastic models.J.R.Statist.Soc,B,1984(46):353-388
[6]Davis M.H.A.Markov models and optimization.London:Chapman and Hall,1993
[7]Hou Zhenting,Liu Zaiming,Zou Jiezhong.QNQL-Process:(H,Q)-process and their Application.Chinese Science Bulletin,1997,42(11):881-886
[8]Hou Zhenting,Liu Zaiming,Zou Jiezhong.Markov skeleton processes.Chinese Science Bulletin,1998,43(11):881-889
[9]侯振挺,郭先平.马尔可夫决策过程.长沙:湖南科学技术出版社,1997
[10]Hou Zhenting.Markov Skeleton Process and applications to queuing systems.Acta,Mathematic Application Sinica,English Series,2002,18(4):537-552
[11]Hou Zhenting,Yuan Chenggui,Zou Jiezhong et al.Transient distribution of the length of GI/G/n queuing systems.Stochastic Analysis and Applications,2003,21(3):567-592
[12]王益民.马尔可夫骨架过程在GI/G/n排队系统中的应用:[博士学位论文].长沙:中南大学,2002
[13]何宁卡.马尔可夫骨架过程的极限理论及其应用:[博士学位论文].长沙:中南大学,2004
[14]蒋放鸣.马尔可夫骨架过程及其应用:[博士学位论文].长沙:中南大学,2004
[15]戴清.马尔可夫骨架过程及其在Frac/G/1排队轮中的应用:[博士学位论文].长沙:中南大学,2004
[16]黄奇.马尔可夫骨架过程在可靠性理论中的应用:[博士学位论文].长沙:中南大学,2004
[17]Hou Zhenting,Liu Guoxing.Markov Skeleton Processes and their applications.Beijing:Science Press,2005
[18]Hou Zhenting,Liu Guoxing.Markov Skeleton Process and their applications.School of Manthematics,Central South University.March 2005
[19]Palm C.Arbetskraftens fordeling rid betjaning av automatckiner.Industritigen Norden,1947(75):75-80,90-94,119-123
[20]Lotka A.J.A contribution to the theory of self-renewing aggregates with special reference to industrial replacement.Ann.Math.Statist,1939(10):1-25
[21]Carnbell N.R.The replacement of perishable members of a continually operating system.J.Roy.Statist 1941(7):110-130
[22]Weibull W.A statistical theory of the strength of materials.Ing.Vetenskaos Akad.Handl.1939(152):1-45
[23]Gumbel E.J.Les vaeurs extremes des distributions statistiques.Annales de I'Institute Henri I' oincare,1935(4):115
[24]Epstein B.Application of the theory of extreme values in fracture problems.J.Amer.Statist Assoc.1948(43):403-412
[25]Barlow R.E.and Proschan F.S.Statistical theory of reliability and life testing,to begin with silver.Springer,MD,1981
[26]曹晋华,程侃.可靠性数学引论.北京:科学出版社,1986
[27]史定华.随机模型的密度演化方法.北京:科学出版社,1999
[28]程侃.寿命分布类与可靠性数学理论.北京:科学出版社,1999
[29]秦英孝.可靠性、维修性、保障性概论.北京:国防工业出版社,2002
[30]曹晋华,程侃.使用和修理有优先权的两部件冷贮备系统的可靠性分析.上海铁道学院学报,1981(4):31-45
[31]刘鸣,苏保河.修理工多重休假两部件冷贮备可修系统.石家庄铁道学院学报,1994,7(3):47-52
[32]唐应辉,刘燕.修理延迟的两个不同型部件冷贮备系统.电子科技大学学报,2004,33(3):331-333
[33]李伟,史定华.具有p_1优先使用权和p_2优先修理权的一半两部件冷贮备系统分析.数理统计与应用概率,1994,9(3):85-98
[34]徐光辉.随机服务系统.北京:科学出版社,1988
[35]周永卫.数学模型中的马尔可夫骨架过程方法:[硕士学位论文].长沙:中南大学,2005
[36]范贺花.马尔可夫骨架过程在数学模型中的应用:[硕士学位论文]. 长沙:中南大学,2005
[37]姜启源,谢金星,叶俊.数学模型.北京:高等教育出版社,2003
[38]唐应辉,刘晓云.一种新型的单部件可修系统.系统工程理论与实践,2003(7):106-109
[39]刘宝友.两不同部件冷贮备可修系统的可靠性分析.石家庄铁道学院学报,1994,7(4):44-50
[40]苏保河.冷贮备可修系统的一个模型及其经济分析.数学的实践与认识,1996,26(4):351-35
[41]周家良,王乃鹏.修理设备可更换的两部件并联可修系统的可靠性分析.工程数学学报,1994,11(4):73-80
[42]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
[43]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,2005,22(1):1-8
[44]吴清太,叶尔骅.开关寿命连续型二部件温贮备可修系统的可靠性分析.应用概率统计,2001,17(2):175-179
[45]科学出版社名词室编.新英汉数学词汇.北京:科学出版社,2002
[46]Zhang,H.et al,"Strong periodicity of monotone transition functions,"Statistic & Probability Letters,55,pp.63-69,2001.
[47]K.Thiruvengdan,Queueing with breakdown,Opns.Res.11,62-71(1963).
[48]Zhang,H.et al,"Strong periodicity of monotone transition functions,"Statistic & Probability Letters,55,pp.63-69,2001.
[49]Fort,G.and Moulines,E.Polynomial ergodicity of Markov transition kernels.Stoch.Proc.Appl.103,57-99(2003)
[50]Meyn,S.P.and Tweedier,R.L.Computable bounds for geometric convergence rates of Marko chains.Ann.Appl.Prob.4,981-1011(1994)
[51]Soulier,PH.,Douc,R.,Fort,G.,and Moulines,E.Practical drift conditions for subgeometricrates of convergence.Ann.Appl.Prob.14(3),1353-1377(2004)
[52]Jarner,S.and Roberts,G.Polynomial convergence rates of Markov chains.Ann.Appl.Prob.12,224-247(2001)
[53]Gut,A.On the moments of some first passage times for sums of dependent random variables.Stoch.Proc.Appl.2,115-126(1974)
[54]Zhang,H.et al,"Strong periodicity of monotone transition functions,"Statistic & Probability Letters,55,pp.63-69,2001.
[55]R.E.Barlow and L.C.Hunter,Reliability analysis of a one-unit system.Opns.Res.19,200-208(1961).
[56]Tang Y H.Some new results on one unit repairable system[J].Microelectronics & Reliability,1996;(36):199-202
[57]K.Thiruvengdan,Queueing with breakdown,Opns.Res.11,62-71(1963).
[58]Y.H.Tang,Some reliability problems arising in GI/G/1 queueing system with repairable service station,Microelectron.Reliab.35,707-712(1995).
[59]R.E.Barlow and L.C.Hunter,Reliability analysis of a one-unit system.Opns.Res.19,200-208(1961).
[60]Hou,Z.T.and Liu,Y.Y.Explicit criteria for several types of ergodicity of the embeddedM/G/1 and GI/M/n queues.J.App.Prob.41,778-790(2004)
[61]逯昭义,环形LAN多令牌存取方式的排队模型.通信学报,1991,12(5):15-21.
[62]R.E.Barlow and L.C.Hunter,Reliability analysis of a one-unit system.Opns.Res.19,200-208(1961).
[63]K.Thiruvengdan,Queueing with breakdown,Opns.Res.11,62-71(1963).