一并联可修系统的可靠性模型
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摘要
可靠性理论是以产品地寿命特征为主要研究对象地边缘性学科,其中一个重要研究方向是可修系统地建摸分析。而两个同型部件并联组成的可修系统是可靠性理论中的最基本模型之一。本文在现有可靠性研究成果的基础上,对以下两个两同型部件并联可修系统的可靠性进行了分析:
考虑检测周期的两同型部件并联可修系统。假定系统的两个部件相同且相互互独立,每个部件都具有正常、异常和故障三个状态(其中正常和异常状态是工作状态),部件依次由正常经过异常到达故障状态,系统工作时,必须通过检测才知道部件是处于正常还是异常状态,并且部件的寿命、修理时间均服从指数分布。本文给出了一个系统模型,然后利用全概率分析、补充变量法等方法和Laplace变换、Laplace-Stieltjes换等工具,求得了系统的一系列重要可靠性数量指标,包括系统的瞬时可用度、系统的稳态可用度、系统的1型异常频度、系统的2型异常频度、系统的1型故障频度、系统的2型故障频度和检测频度,以及系统最优检测周期的计算方法.
The two identical components paralleled repairable system is one of the basic modes in the theory of reliability.On the base of the existing research harvest,this paper has studied the reliability analysis of two systems as follows:
A two identical components paralleled repairable system with inspection cycle. It is assumed that each component of the system has normal,abnormal and failurethree modes(the normal mode and abnormal mode both are operative mode),and none component of the system can attain the failure mode without passing through the abnormal mode,and the system is checked to make sure the components are in normal mode or abnormal mode if it is operating,and the component’s life,its repair time both have exponential distribution.By using total probability decomposition,the supplement variable method,Lapace transform and Lapace-stietjes transform,a series of important reliability characteristics are obtained,such as the system’s instantaneous availability,steady-state availability,the abnormal frequency,and the failure frequency, and the method of calculating the optimal inspection cycle is obtained,too.
考虑检测周期的两同型部件并联可修系统。假定系统的两个部件相同且相互互独立,每个部件都具有正常、异常和故障三个状态(其中正常和异常状态是工作状态),部件依次由正常经过异常到达故障状态,系统工作时,必须通过检测才知道部件是处于正常还是异常状态,并且部件的寿命、修理时间均服从指数分布。本文给出了一个系统模型,然后利用全概率分析、补充变量法等方法和Laplace变换、Laplace-Stieltjes换等工具,求得了系统的一系列重要可靠性数量指标,包括系统的瞬时可用度、系统的稳态可用度、系统的1型异常频度、系统的2型异常频度、系统的1型故障频度、系统的2型故障频度和检测频度,以及系统最优检测周期的计算方法.
The two identical components paralleled repairable system is one of the basic modes in the theory of reliability.On the base of the existing research harvest,this paper has studied the reliability analysis of two systems as follows:
A two identical components paralleled repairable system with inspection cycle. It is assumed that each component of the system has normal,abnormal and failurethree modes(the normal mode and abnormal mode both are operative mode),and none component of the system can attain the failure mode without passing through the abnormal mode,and the system is checked to make sure the components are in normal mode or abnormal mode if it is operating,and the component’s life,its repair time both have exponential distribution.By using total probability decomposition,the supplement variable method,Lapace transform and Lapace-stietjes transform,a series of important reliability characteristics are obtained,such as the system’s instantaneous availability,steady-state availability,the abnormal frequency,and the failure frequency, and the method of calculating the optimal inspection cycle is obtained,too.
引文
[1]曹晋华,程侃.可靠性数学引论.北京:科学出版社.1986
[2]徐维新.可靠性与维修管理基础.北京:兵器出版社,1989
[3]程侃.寿命分布类与可靠性数学引论.北京:科学出版社,1999
[4]梅启智等.系统可靠性工程基础.北京:科学出版社,1987
[5]黄祥瑞.可靠性工程.北京:清华大学出版社,1990
[6]《可靠性文集》编译组.可靠性文集.北京:航空工业出版社,1989
[7]史定华.随机模型的密度演化方法.北京:科学出版社,1999
[8]顾瑛.可靠性工程数学.北京:电子工业出版社,2004
[9] Patrick D.T.O’Connor等.实用可靠性工程(第四版).北京:电子工业出版社,2005
[10]高社生,张玲霞.可靠性理论与工程应用.北京:国防工业出版社.2002
[11]郭波,武小悦,张秀斌等.系统可靠性分析.长沙:国防科技大学出版社.2002
[12] Ross S.M.Stochastic Processes.John Wiley&Sons,1983
[13]郭永基.可靠性工程原理.北京:清华大学出版社,施普林格出版社,2002
[14]陈邵宪.可靠性概论.广东:华飞科技出版社,1985
[15]唐应辉,唐小我.排队论—基础及应用.成都:电子科技大学出版社,2000
[16]朱庆棠,陈良均.随机过程及应用.成都:电子科技大学出版社,1996
[17]王少萍.可靠性工程.北京:北京航空航天大学出版社,2000
[18]张国栋等.系统可靠性与维修性的分析与统计.北京:北京航空航天大学出版社,1990
[19] Ohashi,M.and T.Nishida,A Two-unit Paralleled System wth General Distribution,J.OPer. Res.Japan,23(1980),313一325
[20] Tieling Zhang,Michio Horigome.Availability and reliability of system with dependentcom -ponents and time-varying failure and repair rates.IEEE.Trans.Reliab.50(2),2001,151-158.
[21] Ibe O.C,Wein A.S.Availability systems with partially observable failures.IEEE.Trans.Reliab. 1991,41(1),92-96
[22] S.M.Gupta,N.K.Jaiswal and L.R.Goel,Reliability analysis of a two-unit cold stand by redundant system with two operating modes,Microelectron.Reliab.22,747-759(1985)
[23] YingHui Tang.Some New Reliability Problems And Results For One-unit Repairable System.Microelection.Reliab.1996,36(4):465-4568
[24] Schneeweiss W.G.Duration of hidden faults in randomly checked systems.IEEE Trans. Reliab.1997.26(3).328-330.
[25] Su Baohe.On a two-dissimilar-unit system with three modes and random check. Microelectron.Reliab..1997.37(8).1233-1238
[26] Luss H.An inspection policy model for production facilities.Management Science, 1983, 29:1101-1109
[27] Li Wei,Shi Dinghua.Reliability analysis of a two-unit parallel system with“preemptive priority”rule.Microelectron&Rel,1993,33:1447-145
[28] Mokaddis G.S.Elias S.S.and Labib S.W.On a two-dissimilar-unit standby system with three modes and administrative delay in repair.Microelectron.Rel.1989,29,511-515
[29] Tuteja R.K.Malik S.C.,Reliability and profit analysis of two single-unit models with three modes and different repair polices of repairmen who appear and disappear randomly. Microelectron.Rel.1992,32,351-356
[30] Adachi K,Nishida T.An optimum inspection policy for a one-unit system with preventive maintenance.J.Oper.Res.Soc.Japan,1983,26,105-116
[31] Palm,C.,Arbetsktaftens fordelning vid betjaning av automatckiner.Industritidningen Norden, 75(1947),75-80,90-94,119-123
[32] Lotka,A.J.,A contribution to the theory of self-renewing aggregates with special reference to industrial replacement,Ann.Math.Statist.,10(1939),1-25
[33] Cinlar,E,Introduction to Stochastic processes,Prentice-Hall,Inc,1975
[34] Campbell,N.R.,The replacement of perishable members of a continually operating system.J. Roy.Statist.Soc.,7(1941),110-130
[35] D.k.Pandey and S.M.Gupta,Analysis of two-unit standby redundant system with administrative delay in repair,Microelectron.Reliab.25,917-920(1985)
[36] G.S.Mokaddis,S.S.Elias and S.W.Labib,On a two-dissimilar-unit standby system with three modes and administrative delay in repair,Microelectron.Reliab.29,511-515(1989)
[37] Cox,D.R.,The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables.Proc.Camb.Phil.Soc.51,433-441(1955)
[38]苏保河.一类可修系统的可靠性指标和最优检测策略.自动化学报,2002,28(1):116-119
[39]唐应辉,赵玮.可修排队系统可靠性指标的分解特性.运筹学学报,2004,8(4):73-84
[40]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
[41]沈玉波,冯敬海.两类双部件并联系统的可靠性模型分析.大连理工大学学报,1999,39(1):1-5
[42]张元林,汪风泉,吴少敏.两个不同部件并联可修系统的可靠性分析.东南大学学报,1995,24(5):71-78
[43]陈劲林,杨士元,胡东成.考虑故障检测率的可维修k/n(G)系统的可靠性研究.清华大学学报(自然科学版),1998,38(3):82-85
[44]苏保河,高博.两部件并联可修系统的一个模型.河北师范大学学报,1995,19(3):16-20
[45]孙海珍,苏保河.具有休假的两部件并联可修系统的可靠度.石家庄铁道学院学报,1996,9 (4):21-24
[46]苏保河.系统可靠性与最优检测周期的综合研究.应用数学与计算数学学报,1998,12(1),29-36
[47]周家良,王乃鹏.修理设备可更换的两部件并联系统的可靠性分析.工程数学学报,1994,11(4):73-80
[48]苏保河.非瞬时检测系统的最优检测策略.系统工程学报,2001,16(2):128-132
[49]苏保河,林福永,何敏.2部件串联系统的可靠性与最优检测周期.系统工程,2002,20(6):77-81
[50]史定华.计算可修系统在(0,t]中平均故障次数的新方法.应用数学学报,1985,8(1): 101-110
[56]唐应辉,刘晓云.间歇开放系统的可靠性分析与数值计算.电子科技大学学报,1995,24(3):308-312
[52]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
[53]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):106-111
[54]毛勇,李才良,唐应辉.修理延迟的单部件系统的可靠性分析.电子科技大学学报,2000,29(5):545-548
[55]李才良,蒲冰远,唐应辉等.两不同部件冷储备系统的可靠性分析.电子科技大学学报,2003,32(4):447-450
[56]唐应辉,喻国建,李才良.修理延迟的n部件串联系统的可靠性分析.电子科技大学学报,2003,32(4):451-454
[57]苏保河.被检测系统的可靠性和最优检测策略.运筹学学报.2007,11(1):93-101
[2]徐维新.可靠性与维修管理基础.北京:兵器出版社,1989
[3]程侃.寿命分布类与可靠性数学引论.北京:科学出版社,1999
[4]梅启智等.系统可靠性工程基础.北京:科学出版社,1987
[5]黄祥瑞.可靠性工程.北京:清华大学出版社,1990
[6]《可靠性文集》编译组.可靠性文集.北京:航空工业出版社,1989
[7]史定华.随机模型的密度演化方法.北京:科学出版社,1999
[8]顾瑛.可靠性工程数学.北京:电子工业出版社,2004
[9] Patrick D.T.O’Connor等.实用可靠性工程(第四版).北京:电子工业出版社,2005
[10]高社生,张玲霞.可靠性理论与工程应用.北京:国防工业出版社.2002
[11]郭波,武小悦,张秀斌等.系统可靠性分析.长沙:国防科技大学出版社.2002
[12] Ross S.M.Stochastic Processes.John Wiley&Sons,1983
[13]郭永基.可靠性工程原理.北京:清华大学出版社,施普林格出版社,2002
[14]陈邵宪.可靠性概论.广东:华飞科技出版社,1985
[15]唐应辉,唐小我.排队论—基础及应用.成都:电子科技大学出版社,2000
[16]朱庆棠,陈良均.随机过程及应用.成都:电子科技大学出版社,1996
[17]王少萍.可靠性工程.北京:北京航空航天大学出版社,2000
[18]张国栋等.系统可靠性与维修性的分析与统计.北京:北京航空航天大学出版社,1990
[19] Ohashi,M.and T.Nishida,A Two-unit Paralleled System wth General Distribution,J.OPer. Res.Japan,23(1980),313一325
[20] Tieling Zhang,Michio Horigome.Availability and reliability of system with dependentcom -ponents and time-varying failure and repair rates.IEEE.Trans.Reliab.50(2),2001,151-158.
[21] Ibe O.C,Wein A.S.Availability systems with partially observable failures.IEEE.Trans.Reliab. 1991,41(1),92-96
[22] S.M.Gupta,N.K.Jaiswal and L.R.Goel,Reliability analysis of a two-unit cold stand by redundant system with two operating modes,Microelectron.Reliab.22,747-759(1985)
[23] YingHui Tang.Some New Reliability Problems And Results For One-unit Repairable System.Microelection.Reliab.1996,36(4):465-4568
[24] Schneeweiss W.G.Duration of hidden faults in randomly checked systems.IEEE Trans. Reliab.1997.26(3).328-330.
[25] Su Baohe.On a two-dissimilar-unit system with three modes and random check. Microelectron.Reliab..1997.37(8).1233-1238
[26] Luss H.An inspection policy model for production facilities.Management Science, 1983, 29:1101-1109
[27] Li Wei,Shi Dinghua.Reliability analysis of a two-unit parallel system with“preemptive priority”rule.Microelectron&Rel,1993,33:1447-145
[28] Mokaddis G.S.Elias S.S.and Labib S.W.On a two-dissimilar-unit standby system with three modes and administrative delay in repair.Microelectron.Rel.1989,29,511-515
[29] Tuteja R.K.Malik S.C.,Reliability and profit analysis of two single-unit models with three modes and different repair polices of repairmen who appear and disappear randomly. Microelectron.Rel.1992,32,351-356
[30] Adachi K,Nishida T.An optimum inspection policy for a one-unit system with preventive maintenance.J.Oper.Res.Soc.Japan,1983,26,105-116
[31] Palm,C.,Arbetsktaftens fordelning vid betjaning av automatckiner.Industritidningen Norden, 75(1947),75-80,90-94,119-123
[32] Lotka,A.J.,A contribution to the theory of self-renewing aggregates with special reference to industrial replacement,Ann.Math.Statist.,10(1939),1-25
[33] Cinlar,E,Introduction to Stochastic processes,Prentice-Hall,Inc,1975
[34] Campbell,N.R.,The replacement of perishable members of a continually operating system.J. Roy.Statist.Soc.,7(1941),110-130
[35] D.k.Pandey and S.M.Gupta,Analysis of two-unit standby redundant system with administrative delay in repair,Microelectron.Reliab.25,917-920(1985)
[36] G.S.Mokaddis,S.S.Elias and S.W.Labib,On a two-dissimilar-unit standby system with three modes and administrative delay in repair,Microelectron.Reliab.29,511-515(1989)
[37] Cox,D.R.,The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables.Proc.Camb.Phil.Soc.51,433-441(1955)
[38]苏保河.一类可修系统的可靠性指标和最优检测策略.自动化学报,2002,28(1):116-119
[39]唐应辉,赵玮.可修排队系统可靠性指标的分解特性.运筹学学报,2004,8(4):73-84
[40]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
[41]沈玉波,冯敬海.两类双部件并联系统的可靠性模型分析.大连理工大学学报,1999,39(1):1-5
[42]张元林,汪风泉,吴少敏.两个不同部件并联可修系统的可靠性分析.东南大学学报,1995,24(5):71-78
[43]陈劲林,杨士元,胡东成.考虑故障检测率的可维修k/n(G)系统的可靠性研究.清华大学学报(自然科学版),1998,38(3):82-85
[44]苏保河,高博.两部件并联可修系统的一个模型.河北师范大学学报,1995,19(3):16-20
[45]孙海珍,苏保河.具有休假的两部件并联可修系统的可靠度.石家庄铁道学院学报,1996,9 (4):21-24
[46]苏保河.系统可靠性与最优检测周期的综合研究.应用数学与计算数学学报,1998,12(1),29-36
[47]周家良,王乃鹏.修理设备可更换的两部件并联系统的可靠性分析.工程数学学报,1994,11(4):73-80
[48]苏保河.非瞬时检测系统的最优检测策略.系统工程学报,2001,16(2):128-132
[49]苏保河,林福永,何敏.2部件串联系统的可靠性与最优检测周期.系统工程,2002,20(6):77-81
[50]史定华.计算可修系统在(0,t]中平均故障次数的新方法.应用数学学报,1985,8(1): 101-110
[56]唐应辉,刘晓云.间歇开放系统的可靠性分析与数值计算.电子科技大学学报,1995,24(3):308-312
[52]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
[53]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):106-111
[54]毛勇,李才良,唐应辉.修理延迟的单部件系统的可靠性分析.电子科技大学学报,2000,29(5):545-548
[55]李才良,蒲冰远,唐应辉等.两不同部件冷储备系统的可靠性分析.电子科技大学学报,2003,32(4):447-450
[56]唐应辉,喻国建,李才良.修理延迟的n部件串联系统的可靠性分析.电子科技大学学报,2003,32(4):451-454
[57]苏保河.被检测系统的可靠性和最优检测策略.运筹学学报.2007,11(1):93-101