威布尔分布无失效数据可靠度的点估计和置信下限区间估计
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摘要
针对威布尔分布在无失效数据场合下可靠度的点估计和区间估计进行了研究.首先采用E-Bayes估计得到了威布尔分布无失效数据的失效概率pi的点估计,再用加权最小二乘法实现对威布尔分布参数的点估计从而得到可靠度的点估计.然后利用失效概率pi的后验分布π(pi|si)得到了pi的置信水平为1-α的置信上限piBu的估计,基于配分布曲线法从而得到了可靠度在置信水平为1-α的置信下限RL的估计.
The point estimation and interval estimation of the reliability of Weibull distribution in the case of zero failure data are studied.First,by means of E-Bayes estimation,the point estimation of failure probability piof Weibull distribution with zero failure data was worked out,and then through the method of weighted least squares,the point estimation of the Weibull distribution parameters is realized and thus the point estimation of reliability is obtained.Next,by aid of the posterior distributionπ(pi|si)of the failure probability pi,the point estimation of piwhose upper confidence limit is piBu when the confidence level is at 1-αis obtained.Based on the distribution curve method,the estimation of the lower confidence limit RLwhen its conficence level is at 1-α.
The point estimation and interval estimation of the reliability of Weibull distribution in the case of zero failure data are studied.First,by means of E-Bayes estimation,the point estimation of failure probability piof Weibull distribution with zero failure data was worked out,and then through the method of weighted least squares,the point estimation of the Weibull distribution parameters is realized and thus the point estimation of reliability is obtained.Next,by aid of the posterior distributionπ(pi|si)of the failure probability pi,the point estimation of piwhose upper confidence limit is piBu when the confidence level is at 1-αis obtained.Based on the distribution curve method,the estimation of the lower confidence limit RLwhen its conficence level is at 1-α.
引文
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[12]贾祥,王小林,郭波.极少失效数据和无失效数据的可靠性评估[J].机械工程学报,2016,52(2):182-188.
[13]熊莲花,张玲玲.无失效数据失效率的综合多层Bayes估计[J].山西师范大学学报,2007,21(3),23-27.
[14]韩明.多层先验分布的构造及其应用[J].运筹与管理,1997,6(3):32-40.
[15]韩明.参数的E-Bayes估计法及其应用[J].数学的实践与认识,2004,34(9):97-106.
[16]茆诗松,夏剑峰,管文琪.轴承寿命实验中无失效数据的处理[J].应用统计概率,1993,9(3):326-331.
[17]韩明.指数分布无失效数据的Bayes估计多层Bayes估计[J].宁波大学学报,1995,8(2):9-16.
[2]杨志煊,赵永强,彭秀云.威布尔模型的E-Bayes和多层Bayes估计比较[J].内蒙古工业大学学报,2016,35(4):254-260.
[3]宁江凡.液体火箭发动机无失效条件下的可靠性评估方法研究[D].长沙:国防科技技术大学,2005.
[4]蒋同斌.基于威布尔分布的无失效数据的可靠性分析[J].金陵科技学院学报,2005,21(3):9-13.
[5]茆诗松,罗朝斌.无失效数据的可靠性分析[J].数理统计与应用概率,1989,4(4):489-506.
[6]刘海涛,张志华.威布尔分布无失效数据的Bayes可靠性分析[J].系统工程理论与实践,2008,28(11):103-108.
[7]熊莲花,赵德勤.Weibull分布无失效数据失效概率的估计[J].大学数学,2010,26(3):23-27.
[8]徐天群,陈跃鹏,徐天河,等.威布尔分布场合下无失效数据的可靠性参数估计[J].统计与决策,2012(13):17-20.
[9]蔡忠义,陈云翔,项华春,等.基于无失效数据的加权E-Bayes可靠性评估方法[J].系统工程与电子技术,2015,37(1):219-223.
[10]陈家鼎,孙万龙,李补喜.关于无失效数据下的置信限[J].应用数学学报,1995,18(1):90-100.
[11]韩明.Weibull分布可靠性参数的置信限[J].机械强度,2009,31(1):59-62.
[12]贾祥,王小林,郭波.极少失效数据和无失效数据的可靠性评估[J].机械工程学报,2016,52(2):182-188.
[13]熊莲花,张玲玲.无失效数据失效率的综合多层Bayes估计[J].山西师范大学学报,2007,21(3),23-27.
[14]韩明.多层先验分布的构造及其应用[J].运筹与管理,1997,6(3):32-40.
[15]韩明.参数的E-Bayes估计法及其应用[J].数学的实践与认识,2004,34(9):97-106.
[16]茆诗松,夏剑峰,管文琪.轴承寿命实验中无失效数据的处理[J].应用统计概率,1993,9(3):326-331.
[17]韩明.指数分布无失效数据的Bayes估计多层Bayes估计[J].宁波大学学报,1995,8(2):9-16.