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摘要: 推导了四单元混联系统屏蔽数据场合下的似然函数,并且给出了常数失效率单元和线性失效率单元所组成的四单元混联系统屏蔽数据的参数的极大似然估计,以及采用似然比构造区间估计的方法得到参数的近似区间估计.
关键词: 屏蔽数据; 四单元混联系统; 极大似然估计; 近似区间估计
中图分类号: O 213 文献标志码: A 文章编号: 10005137(2017)02017808
Abstract: The likelihood function of fourunit hybrid system is deduced based on masked data.The maximum likelihood estimates of parameters are proposed for hybrid system composed of four units with constant failure rate and linear failure rate based on masked data.Besides,the approximate interval estimates of parameters are obtained by using likelihood ratio to construct interval estimate.
Key words: masked data; fourunit hybrid system; maximum likelihood estimate; approximate interval estimate
0 引 言
在可靠性分析中,人们往往通过分析系统的寿命数据来估计该系统中各组成单元寿命分布中的未知参数.系统寿命试验数据包括两个方面.一是失效时间;二是失效原因.理想状态下,系统的寿命数据应该包括系统失效的具体时间以及由哪个单元失效导致整个系统失效的信息.但大多数时候,导致系统失效的那个单元并不能够被准确识别出来,人们仅能够把导致系统失效的原因归结为某些单元所组成的一个集合,系统真正失效的原因被屏蔽掉了.在现实生活中,由于故障诊断和故障检测所需的费用昂贵,特别是在现代系统中越来越多地采用模块化设计,引起系统失效的确切单元通常都是未知的.在對计算机或集成电路等进行系统可靠性研究时,也会遇到相类似的屏蔽问题.导致屏蔽发生的原因很多,如:经费的不足、时间的限制、记录的错误、诊断工具的缺乏,及某些单元失效所带来的破坏性后果等.这使得屏蔽数据的统计分析成为近年来研究的热点问题,许多学者做了很好的工作,并取得了一系列研究成果,具体见文献[1-21].
值得指出的是,随着系统的功能越来越完善,其构成也越来越复杂,例如航空电源系统或雷达系统等,不再是单纯的串联或并联系统,而更多的是多单元的混联复杂系统,且常常伴有屏蔽现象发生.关于由4个单元组成的系统,除了4个单元全部串联和4个单元全部并联外,系统还有6种不同的构成方式,将其统称为四单元混联系统.图1即为4个单元组成的混联系统的一种.
本文作者详细推导了如图1所示的四单元混联系统屏蔽数据场合下的似然函数,并且给出了常数失效率单元和线性失效率单元所组成的四单元混联系统屏蔽数据的参数的极大似然估计,并采用似然比构造区间估计的方法得到参数的近似区间估计.
参考文献:
[1] Usher J S,Hodgson T J.Maximum likelihood analysis of component reliability using masked system lifetest data [J].IEEE Transactions on Reliability,1988,37(5):550-555.
[2] Doganaksoy N.Interval estimation from censored & masked systemfailure data [J].IEEE Transactions on Reliability,1991,40(3):280-286.
[3] Lin Dennis K J,Usher J S,Guess F M.Exact maximum likelihood estimation using masked system data [J].IEEE Transactions on Reliability,1993,42(4):631-635.
[4] Reiser B,Guttman I,Lin Dennis K J,et al.Bayesian inference for masked system lifetime data [J].Appl Statist,1995,44(1):79-90.
[5] Usher J S.Weibull component reliability—prediction in the presence of masked data [J].IEEE Transactions on Reliability,1996,45(2):229-232.
[6] Lin Dennis K J,Usher J S,Guess F M.Bayes estimation of componentreliability from masked systemlife data [J].IEEE Transactions on Reliability,1996,45(2):233-237.
[7] Sarhan A M.Reliability estimations of components from masked system life data [J].Reliability Engineering and System Safety,2001,74:107-113. [8] Sarhan A M.The bayes procedure in exponential reliability family models using conjugate convex tent prior family [J].Reliability Engineering and System Safety,2001,71:97-102.
[9] Sarhan A M.Estimation of system components reliabilities using masked data [J].Applied Mathematics and Computation,2003,136:79-92.
[10] Sarhan A M,Ahmed H.ElBassiouny.Estimation of components reliability in a parallel system using masked system life data [J].Applied Mathematics and Computation,2003,138:61-75.
[11] Sarhan A M,Awad I ElGohary.Estimations of parameters in Pareto reliability model in the presence of masked data [J].Reliability Engineering and System Safety,2003,82:75-83.
[12] Sarhan A M.Parameter Estimations in linear failure rate model using masked data [J].Applied Mathematics and Computation,2004,151:233-249.
[13] Sarhan A M.Parameter Estimations in a general hazard rate model using masked data [J].Applied Mathematics and Computation,2004,153:513-536.
[14] Sarhan A M.Bayes estimations for reliability measures in geometric distribution model using masked system life test data [J].Computational Statistics and Data Analysis,2008,52(4):1821-1836.
[15] Awad ElGohary.Bayesian estimation of the parameters in two nonindependent component series system with dependent time failure rate [J].Applied Mathematics and Computation,2004,154:41-51.
[16] Hutto D E,Mazzuchi T,Sarkani S.Analysis of reliability using masked system life data [J].International Journal of Quality & Reliability Management,2009,26(7):723-739.
[17] Tsai H F,Wan L W.Accelerated life tests for weibull series systems with masked data [J].IEEE Transactions on Reliability,2011,60(3):557-569.
[18] Hou H L,Jiang Y W,Shi Y M.Parameter estimations in BurrXII model using masked data [J].Chin Quart J of Math,2011,26(2):251-255.
[19] Xu A C,Tang Y C.Bayesian analysis of pareto reliability with dependent masked data [J].IEEE Transactions on Reliability,2009,58(4):583-588.
[20] Wang R H,Xu X L,Gu B Q.The statistical analysis of parallel system for TypeI censored test using masked data [C].Recent Advance in Statistics Application and Related Areas2nd Conference of the International Institute of Applied Statistics Studies,Qingdao,China,July 24-29,2009,789-795.
[21] Xu A C,Tang Y C.An overview on statistical analysis for masked system lifetime data [J].Chinese Journal of Applied Probability and Statistics,28(4):380-388.
(責任编辑:冯珍珍)
关键词: 屏蔽数据; 四单元混联系统; 极大似然估计; 近似区间估计
中图分类号: O 213 文献标志码: A 文章编号: 10005137(2017)02017808
Abstract: The likelihood function of fourunit hybrid system is deduced based on masked data.The maximum likelihood estimates of parameters are proposed for hybrid system composed of four units with constant failure rate and linear failure rate based on masked data.Besides,the approximate interval estimates of parameters are obtained by using likelihood ratio to construct interval estimate.
Key words: masked data; fourunit hybrid system; maximum likelihood estimate; approximate interval estimate
0 引 言
在可靠性分析中,人们往往通过分析系统的寿命数据来估计该系统中各组成单元寿命分布中的未知参数.系统寿命试验数据包括两个方面.一是失效时间;二是失效原因.理想状态下,系统的寿命数据应该包括系统失效的具体时间以及由哪个单元失效导致整个系统失效的信息.但大多数时候,导致系统失效的那个单元并不能够被准确识别出来,人们仅能够把导致系统失效的原因归结为某些单元所组成的一个集合,系统真正失效的原因被屏蔽掉了.在现实生活中,由于故障诊断和故障检测所需的费用昂贵,特别是在现代系统中越来越多地采用模块化设计,引起系统失效的确切单元通常都是未知的.在對计算机或集成电路等进行系统可靠性研究时,也会遇到相类似的屏蔽问题.导致屏蔽发生的原因很多,如:经费的不足、时间的限制、记录的错误、诊断工具的缺乏,及某些单元失效所带来的破坏性后果等.这使得屏蔽数据的统计分析成为近年来研究的热点问题,许多学者做了很好的工作,并取得了一系列研究成果,具体见文献[1-21].
值得指出的是,随着系统的功能越来越完善,其构成也越来越复杂,例如航空电源系统或雷达系统等,不再是单纯的串联或并联系统,而更多的是多单元的混联复杂系统,且常常伴有屏蔽现象发生.关于由4个单元组成的系统,除了4个单元全部串联和4个单元全部并联外,系统还有6种不同的构成方式,将其统称为四单元混联系统.图1即为4个单元组成的混联系统的一种.
本文作者详细推导了如图1所示的四单元混联系统屏蔽数据场合下的似然函数,并且给出了常数失效率单元和线性失效率单元所组成的四单元混联系统屏蔽数据的参数的极大似然估计,并采用似然比构造区间估计的方法得到参数的近似区间估计.
参考文献:
[1] Usher J S,Hodgson T J.Maximum likelihood analysis of component reliability using masked system lifetest data [J].IEEE Transactions on Reliability,1988,37(5):550-555.
[2] Doganaksoy N.Interval estimation from censored & masked systemfailure data [J].IEEE Transactions on Reliability,1991,40(3):280-286.
[3] Lin Dennis K J,Usher J S,Guess F M.Exact maximum likelihood estimation using masked system data [J].IEEE Transactions on Reliability,1993,42(4):631-635.
[4] Reiser B,Guttman I,Lin Dennis K J,et al.Bayesian inference for masked system lifetime data [J].Appl Statist,1995,44(1):79-90.
[5] Usher J S.Weibull component reliability—prediction in the presence of masked data [J].IEEE Transactions on Reliability,1996,45(2):229-232.
[6] Lin Dennis K J,Usher J S,Guess F M.Bayes estimation of componentreliability from masked systemlife data [J].IEEE Transactions on Reliability,1996,45(2):233-237.
[7] Sarhan A M.Reliability estimations of components from masked system life data [J].Reliability Engineering and System Safety,2001,74:107-113. [8] Sarhan A M.The bayes procedure in exponential reliability family models using conjugate convex tent prior family [J].Reliability Engineering and System Safety,2001,71:97-102.
[9] Sarhan A M.Estimation of system components reliabilities using masked data [J].Applied Mathematics and Computation,2003,136:79-92.
[10] Sarhan A M,Ahmed H.ElBassiouny.Estimation of components reliability in a parallel system using masked system life data [J].Applied Mathematics and Computation,2003,138:61-75.
[11] Sarhan A M,Awad I ElGohary.Estimations of parameters in Pareto reliability model in the presence of masked data [J].Reliability Engineering and System Safety,2003,82:75-83.
[12] Sarhan A M.Parameter Estimations in linear failure rate model using masked data [J].Applied Mathematics and Computation,2004,151:233-249.
[13] Sarhan A M.Parameter Estimations in a general hazard rate model using masked data [J].Applied Mathematics and Computation,2004,153:513-536.
[14] Sarhan A M.Bayes estimations for reliability measures in geometric distribution model using masked system life test data [J].Computational Statistics and Data Analysis,2008,52(4):1821-1836.
[15] Awad ElGohary.Bayesian estimation of the parameters in two nonindependent component series system with dependent time failure rate [J].Applied Mathematics and Computation,2004,154:41-51.
[16] Hutto D E,Mazzuchi T,Sarkani S.Analysis of reliability using masked system life data [J].International Journal of Quality & Reliability Management,2009,26(7):723-739.
[17] Tsai H F,Wan L W.Accelerated life tests for weibull series systems with masked data [J].IEEE Transactions on Reliability,2011,60(3):557-569.
[18] Hou H L,Jiang Y W,Shi Y M.Parameter estimations in BurrXII model using masked data [J].Chin Quart J of Math,2011,26(2):251-255.
[19] Xu A C,Tang Y C.Bayesian analysis of pareto reliability with dependent masked data [J].IEEE Transactions on Reliability,2009,58(4):583-588.
[20] Wang R H,Xu X L,Gu B Q.The statistical analysis of parallel system for TypeI censored test using masked data [C].Recent Advance in Statistics Application and Related Areas2nd Conference of the International Institute of Applied Statistics Studies,Qingdao,China,July 24-29,2009,789-795.
[21] Xu A C,Tang Y C.An overview on statistical analysis for masked system lifetime data [J].Chinese Journal of Applied Probability and Statistics,28(4):380-388.
(責任编辑:冯珍珍)