部件寿命服从威布尔分布时典型系统的寿命与剩余寿命估计
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摘要
在实际工程中,对系统寿命以及剩余寿命的估计非常重要。在已知系统中部件寿命与可靠度的前提下,关于如何快速得到系统级寿命与剩余寿命的相关研究比较缺乏。针对这一问题,首先研究了可靠度、寿命以及剩余寿命的关系,进一步假设部件寿命服从同一威布尔分布,根据部件的寿命与可靠度函数,推导得到串联、并联和表决系统寿命与剩余寿命期望的封闭表达式,并给出了相应的计算方法。对于冷备系统,当部件寿命服从同一指数分布时,推得了系统寿命及剩余寿命期望的封闭表达式,而当部件寿命服从同一威布尔分布时,给出了系统寿命与剩余寿命的数值计算方法。仿真试验证明本文所提出的方法是准确高效的。最后,以卫星中的动量轮r/n(G)表决系统为例开展了实例研究,证明了该方法在工程实践中的有效性。
In practical engineering,it is significant to estimate the lifetime and residual life of a system.The research is limited for how to obtain the lifetime and residual life of a system efficiently by using the lifetime and reliability of components.Motivated by this problem,relationship between reliability,lifetime and residual life is analyzed in this paper.Further,on the assumption that the components are identically and independently Weibull distributed,the closed-forms for lifetime and residual life of series,parallel and r/n(G)systems are derived based on lifetime and reliability function of components,respectively.And the calculation method is presented accordingly.Next,for the lifetime and residual life of the cold standby system,the closed-form is obtained when the components lifetime are identically exponentially distributed and numerical method is proposed when components follow Weibull distributions.The numerical examples prove the proposed method is accurate and efficient.Finally,ar/n(G)system composed by momentum wheels is taken as an example and the results shows that this method is worth learning in engineering practice.
In practical engineering,it is significant to estimate the lifetime and residual life of a system.The research is limited for how to obtain the lifetime and residual life of a system efficiently by using the lifetime and reliability of components.Motivated by this problem,relationship between reliability,lifetime and residual life is analyzed in this paper.Further,on the assumption that the components are identically and independently Weibull distributed,the closed-forms for lifetime and residual life of series,parallel and r/n(G)systems are derived based on lifetime and reliability function of components,respectively.And the calculation method is presented accordingly.Next,for the lifetime and residual life of the cold standby system,the closed-form is obtained when the components lifetime are identically exponentially distributed and numerical method is proposed when components follow Weibull distributions.The numerical examples prove the proposed method is accurate and efficient.Finally,ar/n(G)system composed by momentum wheels is taken as an example and the results shows that this method is worth learning in engineering practice.
引文
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[13]BAROT D,PATEL M.Bayesian estimation of reliability indexes for cold standby system under general progressive typeⅡcensoring date[J].International Journal of Quality&Reliability Management,2014,31(3):311-343.
[14]LI F.Reliability analysis of a cold standby system under progressive Type-Ⅱcensoring date[J].Advanced Materials Research,2012,459:540-543.
[15]SHI Y M,SHI X L,Reliability estimation for cold standby series system based on general progressive typeⅡcensored samples[J].Advanced Materials Research,2013,321:2460-2463.
[16]JIA X,GUO B.Analysis of non-repairable cold standbysystem in Bayes theory[J].Statistical Computation and Simulation,2017,86(11):2089-2112.
[17]蒋平,邢云燕,程文科,等.可靠性工程[M].北京:国防工业出版社,2015:43-46.JIANG P,XING Y Y,CHENG W K,et al.An introduction to reliability engineering[M].Beijing:National Defense Industry Press,2015:43-46.
[18]ERYILMAZ S,COOLEN F P,COOLEN-MANURI T.Mean residual life of coherent systems consisting of multiple types of dependent components[J].Naval Research Logistics,2018,65(4):86-97.
[19]FENG Y,HUANG X D,HONG R J,et al.Online residual useful prediction of large-size slewing bearings-a data fusion method[J].Journal of Central South University,2017,24(1):114-126.
[20]郭波,武小悦,张秀斌,等.系统可靠性分析[M].长沙:国防科技大学出版社,2002:23-24.GUO B,WU X Y,ZHANG X B,et al.Reliability analysis of system[M].Changsha:National University of Defense Technology Press,2002:23-24.
[21]AMARI S V,DILL G.A new method for reliability analysis of standby systems[C]∥Proc.of the Annual Reliability and Maintainability Symposium,2009:417-422.
[22]LEVITIN G,AMARI S V.Approximation algorithm for evaluating time-to-failure distribution of k-out-of-n system with shared standby elements[J].Reliability Engineering&System Safety,2010,95(4):396-401.
[23]鲁祖亮,曹龙舟,李林.数值计算方法与Matlab程序设计[M].成都:西南交通大学出版社,2017:53-58.LU Z L,CAO L Z,LI L.Numerical calculation method and Matlab programming[M].Chengdu:Southwest Jiaotong University Press,2017:53-58.
[24]陈浩.基于多源信息融合的典型卫星平台分系统剩余寿命预测研究[D].长沙:国防科技大学,2016.CHEN H.Research on residual life prediction for typical satellite platform subsystem based on multi-source information fusion[D].Changsha:National University of Defense Technology,2016.
[25]LI H,PAN D H,CHEN C L P.Reliability modeling and life estimation using an expectation maximum based on Wiener degradation model for momentum wheels[J].IEEE Trans.on Reliability,2015,45(5):955-963.
[26]JIANG L,CHENG Y H,YANG T S,et al.Remaining useful life prediction for the momentum wheel considering work condition switching[C]∥Proc.of the IEEE Chinese Guidance,Navigation and Control Conference,2016.
[27]刘强,黄秀平,周经纶,等.基于失效物理的动量轮贝叶斯可靠性评估[J].航空学报,2009,30(8):1392-1397.LIU Q,HUANG X P,ZHOU J L,et al.Failure-physics-analysis-based method of Bayesian reliability estimation for momentum wheel[J].Acta Aeronautica et Astronautica Sinica,2009,30(8):1392-1397.
[2]李学京,韩筱爽.复杂系统平均寿命综合评估方法研究[J].数学的实践与认识,2007,37(2):110-115.LI X J,HAN X S.An assessment method for the mean life of complex system[J].Mathematics in Practice and Theory,2007,37(2):110-115.
[3]金星,洪延姬,张明亮,等.大型复杂系统平均寿命评定的蒙特卡罗方法[J].系统仿真学报,2005,17(1):66-68.JIN X,HONG Y J,ZHANG M L,et al.Monte Carlo method of MTTF evaluation for large complex system[J].Journal of System Simulation,2005,17(1):66-68.
[4]杨军,赵宇.复杂系统平均剩余寿命综合评估方法[J].航空学报,2007,28(6):1351-1354.YANG J,ZHAO Y.An assessment method for the mean residual life of complex system[J].Acta Aeronautica et Astronautica Sinica,2007,28(6):1351-1354.
[5]陈常顺.平均剩余寿命置信下限的评估[J].中北大学学报,2007,28(3):208-211.CHEN C S.Lower limit assessment of confidence of mean residual life[J].Journal of North University of China,2007,28(3):208-211.
[6]BAYRAMOGLU I,AHSANULLAH M,AKHUNDOV I.A residual life function of a system having parallel or series structures[EB/OL].[2018-12-06].http:∥dm.ieu.edu.tr/Ism/Reliab2.pdf.
[7]ASADI M,BAYRAMOGLU I.A note on the mean residual life function of a parallel system[J].Communications in StatisticsTheory and Methods,2005,34(2):475-485.
[8]SADEGH K.Mean past and mean residual life functions of a parallel system with nonidentical components[J].Communications in Statistics-Theory and Methods,2008,37(7):1134-1145.
[9]MOHAMMAD Z R.Evaluations of the mean residual lifetime of an m-out-of-nsystem[J].Statistics and Probability Letters,2010,80(5/6):333-342.
[10]NAVARRO J,ERYILMAZ S.Mean residual lifetimes of consecutive k-out-of-n systems[J].Journal of Applied Probability,2007,44(1):82-98.
[11]SARHAN A M,ABOUAMMOH A M.Reliability of k-outof-nnonrepairable systems with nonindependent components subjected to common shocks[J].Microelectronics Reliability,2001,41(4):617-621.
[12]ASADI M,BAIRAMOV I.The mean residual life function of a k-out-of-nstructure at the system level[J].IEEE Trans.on Reliability,2006,55(2):314-318.
[13]BAROT D,PATEL M.Bayesian estimation of reliability indexes for cold standby system under general progressive typeⅡcensoring date[J].International Journal of Quality&Reliability Management,2014,31(3):311-343.
[14]LI F.Reliability analysis of a cold standby system under progressive Type-Ⅱcensoring date[J].Advanced Materials Research,2012,459:540-543.
[15]SHI Y M,SHI X L,Reliability estimation for cold standby series system based on general progressive typeⅡcensored samples[J].Advanced Materials Research,2013,321:2460-2463.
[16]JIA X,GUO B.Analysis of non-repairable cold standbysystem in Bayes theory[J].Statistical Computation and Simulation,2017,86(11):2089-2112.
[17]蒋平,邢云燕,程文科,等.可靠性工程[M].北京:国防工业出版社,2015:43-46.JIANG P,XING Y Y,CHENG W K,et al.An introduction to reliability engineering[M].Beijing:National Defense Industry Press,2015:43-46.
[18]ERYILMAZ S,COOLEN F P,COOLEN-MANURI T.Mean residual life of coherent systems consisting of multiple types of dependent components[J].Naval Research Logistics,2018,65(4):86-97.
[19]FENG Y,HUANG X D,HONG R J,et al.Online residual useful prediction of large-size slewing bearings-a data fusion method[J].Journal of Central South University,2017,24(1):114-126.
[20]郭波,武小悦,张秀斌,等.系统可靠性分析[M].长沙:国防科技大学出版社,2002:23-24.GUO B,WU X Y,ZHANG X B,et al.Reliability analysis of system[M].Changsha:National University of Defense Technology Press,2002:23-24.
[21]AMARI S V,DILL G.A new method for reliability analysis of standby systems[C]∥Proc.of the Annual Reliability and Maintainability Symposium,2009:417-422.
[22]LEVITIN G,AMARI S V.Approximation algorithm for evaluating time-to-failure distribution of k-out-of-n system with shared standby elements[J].Reliability Engineering&System Safety,2010,95(4):396-401.
[23]鲁祖亮,曹龙舟,李林.数值计算方法与Matlab程序设计[M].成都:西南交通大学出版社,2017:53-58.LU Z L,CAO L Z,LI L.Numerical calculation method and Matlab programming[M].Chengdu:Southwest Jiaotong University Press,2017:53-58.
[24]陈浩.基于多源信息融合的典型卫星平台分系统剩余寿命预测研究[D].长沙:国防科技大学,2016.CHEN H.Research on residual life prediction for typical satellite platform subsystem based on multi-source information fusion[D].Changsha:National University of Defense Technology,2016.
[25]LI H,PAN D H,CHEN C L P.Reliability modeling and life estimation using an expectation maximum based on Wiener degradation model for momentum wheels[J].IEEE Trans.on Reliability,2015,45(5):955-963.
[26]JIANG L,CHENG Y H,YANG T S,et al.Remaining useful life prediction for the momentum wheel considering work condition switching[C]∥Proc.of the IEEE Chinese Guidance,Navigation and Control Conference,2016.
[27]刘强,黄秀平,周经纶,等.基于失效物理的动量轮贝叶斯可靠性评估[J].航空学报,2009,30(8):1392-1397.LIU Q,HUANG X P,ZHOU J L,et al.Failure-physics-analysis-based method of Bayesian reliability estimation for momentum wheel[J].Acta Aeronautica et Astronautica Sinica,2009,30(8):1392-1397.