基于Weibull分布的恒加载试验置信样本量的可靠性优化设计
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摘要
为实现长寿命、高可靠度产品在正常应力水平时可靠性地快速评估,建立Arrhenius—Weibull可靠性统计模型,假定试验各应力水平下Weibull分布型产品的失效机理保持一致,且特征寿命与试验应力水平间满足对数线性加速寿命试验模型。以产品在正常试验应力水平下中位寿命估计值的方差最小为优化目标,以试验应力水平数和大小,试样分配比例以及试验各应力水平下的截尾时间为设计变量,提出了Weibull分布定时截尾恒加载试验可靠性优化方案。获得了用于构造模型参数渐进置信区间的Fisher信息矩阵。算例分析表明:恒加载试验可靠性优化方案具有可行性。
In order to realize the rapid reliability evaluation of long-life and high reliability products at a normal stress level, the reliability statistical model of Arrhenius—Weibull was established, by using the Weibull distributions products with the consistent failure mechanism and a log-linear acceleration life test model between characteristic life and stress level. The minimum variance of the product median lifetime estimate at normal stress level as optimum object was considered, the number and quantity of test stress level, samples allocation proporation and censoring time at each stress level are determined as design variables, put forward a reliability optimum scheme of time-censoring constant-stress ALT(CSALT) for weibull distributions. The Fisher Information Matrix is obtained for constructing asymptotic confidence intervals for the model parameters. As the example analysis shows that the reliability optimum scheme of CSALT is effective.
In order to realize the rapid reliability evaluation of long-life and high reliability products at a normal stress level, the reliability statistical model of Arrhenius—Weibull was established, by using the Weibull distributions products with the consistent failure mechanism and a log-linear acceleration life test model between characteristic life and stress level. The minimum variance of the product median lifetime estimate at normal stress level as optimum object was considered, the number and quantity of test stress level, samples allocation proporation and censoring time at each stress level are determined as design variables, put forward a reliability optimum scheme of time-censoring constant-stress ALT(CSALT) for weibull distributions. The Fisher Information Matrix is obtained for constructing asymptotic confidence intervals for the model parameters. As the example analysis shows that the reliability optimum scheme of CSALT is effective.
引文
[1] Watkins A J.Review:Likelihood method for fitting weibull log-linear models to accelerated life-test data[J].IEEE Transactions on Reliability,1994,43(3):361-365.
[2] Wang W,Kececioglu D B.Fitting the Weibull log-linear model to accelerated life-test data[J].IEEE Transactions on Reliability,2000,49(2):217-223.
[3] Nelson W,Kielpinski T J.Theory for optimum censored accelerated life tests for normal and lognormal life distributions[J].Technometrics,1976,18(1):105-114.
[4] Nelson W,Meeker W Q.Theory for optimum accelerated censored life tests for Weibull and extreme value distributions[J].Technometrics,1978,20(2):171-177.
[5] Yang G B.Optimum constant-stress accelerated life-test plans[J].IEEE transactions on reliability,1994,43(4):575-581.
[6] Tang L C,Tan A P,Ong S H.Planning accelerated life tests with three constant stress levels[J].Computers & industrial engineering,2002,42(2):439-446.
[7] 陈文华,杨帆,刘俊俊,等.步进应力加速寿命试验方案优化设计理论与方法[J].机械工程学报,2012,48(22):182-187.CHEN WenHua,YANG Fan,LIU JunJun,et al.Theory and Method for Simulation Evaluation of Aeeclerated Life Test Plan under Step-stress[J].Journal of Mechanical Engineering,2012,48(22):182-187(In Chinese).
[8] HassanA M.On the optimal design of failure step-stress partially accelerated life tests for exponentiated inverted Weibull with censoring[J].Australian Journal of Basic and Applied Sciences,2013,7(1):97-104.
[9] 郭宏然.陀螺电机加速寿命试验设计与可靠性分析[D].西安:西安电子科技大学,2014:19-44.GUO HongRan.Design and Reliability Analysis on Accelerated Life Test of Gyroscope Motor[D].Xian:Xidian University,2014:19-44(In Chinese).
[10] Nelson W B.Accelerated testing:statistical models,test plans,and data analysis[M].John Wiley & Sons,2009:82-376.
[11] 茆诗松,王玲玲.加速寿命试验[M].北京:科学出版社,2000:96-118.MAO ShiSong,WANG LingLing.Accelerated Life Tests[M].Beijing:Science Press,2000:96-118(In Chinese).
[12] 茆诗松,王静龙,濮晓龙,等.高等数理统计(第二版)[M].北京:高等教育出版社,2006:83-124.MAO ShiSong,WANG JingLong,PUXiaoLong,et al.Advanced Mathematical Ststistics(Second Edition) [M].Beijing:Higher Education Press,2006:98-108.
[13] Watkins A J,John A M.On constant stress accelerated life tests terminated by Type II censoring at one of the stress levels[J].Journal of Statistical Planning and Inference,2008,138(3):768-786.
[14] Nelson W.Analysis of Accelerated LifeTest Data-Least Squares Methods for the Inverse Power Law Model[J].IEEE Transactions on Reliability,1975,24(2):103-107.
[15] 陈文华,程耀东.威布尔分布下恒定应力加速寿命试验方案的优化设计[J].浙江大学学报(自然科学版),1999,33(4):337-342.CHEN WenHua,CHENG YaoDong.Optimum Design of Constant-Stress Accelerated Life Test Plans for Weibull Life Distributions [J].Journal of Zhejiang University(Natural Science Edition),1999,33(4):337-342(In Chinese).
[2] Wang W,Kececioglu D B.Fitting the Weibull log-linear model to accelerated life-test data[J].IEEE Transactions on Reliability,2000,49(2):217-223.
[3] Nelson W,Kielpinski T J.Theory for optimum censored accelerated life tests for normal and lognormal life distributions[J].Technometrics,1976,18(1):105-114.
[4] Nelson W,Meeker W Q.Theory for optimum accelerated censored life tests for Weibull and extreme value distributions[J].Technometrics,1978,20(2):171-177.
[5] Yang G B.Optimum constant-stress accelerated life-test plans[J].IEEE transactions on reliability,1994,43(4):575-581.
[6] Tang L C,Tan A P,Ong S H.Planning accelerated life tests with three constant stress levels[J].Computers & industrial engineering,2002,42(2):439-446.
[7] 陈文华,杨帆,刘俊俊,等.步进应力加速寿命试验方案优化设计理论与方法[J].机械工程学报,2012,48(22):182-187.CHEN WenHua,YANG Fan,LIU JunJun,et al.Theory and Method for Simulation Evaluation of Aeeclerated Life Test Plan under Step-stress[J].Journal of Mechanical Engineering,2012,48(22):182-187(In Chinese).
[8] HassanA M.On the optimal design of failure step-stress partially accelerated life tests for exponentiated inverted Weibull with censoring[J].Australian Journal of Basic and Applied Sciences,2013,7(1):97-104.
[9] 郭宏然.陀螺电机加速寿命试验设计与可靠性分析[D].西安:西安电子科技大学,2014:19-44.GUO HongRan.Design and Reliability Analysis on Accelerated Life Test of Gyroscope Motor[D].Xian:Xidian University,2014:19-44(In Chinese).
[10] Nelson W B.Accelerated testing:statistical models,test plans,and data analysis[M].John Wiley & Sons,2009:82-376.
[11] 茆诗松,王玲玲.加速寿命试验[M].北京:科学出版社,2000:96-118.MAO ShiSong,WANG LingLing.Accelerated Life Tests[M].Beijing:Science Press,2000:96-118(In Chinese).
[12] 茆诗松,王静龙,濮晓龙,等.高等数理统计(第二版)[M].北京:高等教育出版社,2006:83-124.MAO ShiSong,WANG JingLong,PUXiaoLong,et al.Advanced Mathematical Ststistics(Second Edition) [M].Beijing:Higher Education Press,2006:98-108.
[13] Watkins A J,John A M.On constant stress accelerated life tests terminated by Type II censoring at one of the stress levels[J].Journal of Statistical Planning and Inference,2008,138(3):768-786.
[14] Nelson W.Analysis of Accelerated LifeTest Data-Least Squares Methods for the Inverse Power Law Model[J].IEEE Transactions on Reliability,1975,24(2):103-107.
[15] 陈文华,程耀东.威布尔分布下恒定应力加速寿命试验方案的优化设计[J].浙江大学学报(自然科学版),1999,33(4):337-342.CHEN WenHua,CHENG YaoDong.Optimum Design of Constant-Stress Accelerated Life Test Plans for Weibull Life Distributions [J].Journal of Zhejiang University(Natural Science Edition),1999,33(4):337-342(In Chinese).