基于记录值样本下FW分布的可靠性统计分析
发布时间：2019-06-19 11:26
【摘要】：Bebbington等(2007)提出一个两参数修正的Weibull(简记为FW)分布,该分布具有一个简单的失效率函数.当给定不同参数值时,其失效率可以是单调增加的,亦可以是修正浴盆状的.记录值作为特殊的次序统计量,由于其具有重要的理论意义和应用价值,自提出以来被广泛的应用到可靠性分析等诸多领域.本文主要运用经典方法和Bayes方法研究该分布的可靠性统计分析.首先给出记录值的概念、性质以及似然函数.其次介绍了FW分布失效率的性质并给出WPP图法理论,然后讨论了FW分布参数、可靠度和失效率的回归估计、逆矩估计、MLE以及基于观测信息矩阵下的置信区间,并运用Bootstrap法构造了相应的置信区间.在假定两参数先验为Gamma先验和无信息先验的条件下证明了FW分布参数的满条件后验分布均为对数凹函数,这样就可以运用Gibbs抽样方法来获得Markov Chain Monte Carlo(MCMC)样本,从而做出参数、可靠度和失效率的Bayes估计和后验可信区间.最后通过实例模拟获得各种估计的结果,并基于Bootstrap法和Gibbs抽样法构造的均方误差和置信区间来比较参数、可靠度和失效率的回归估计、逆矩估计、MLE和Bayes估计的优良性.结果表明当选取合适的先验时,Bayes估计优于其他估计,MLE优于逆矩估计和回归估计,而回归估计的精度最差,而且比较基于观测信息矩阵和Bootstrap法得到的置信区间发现基于观测信息矩阵得到的结果较好.第四章主要基于记录值样本研究FW分布的可靠性统计.首先给出参数、可靠度和失效率的MLE,并基于观测信息矩阵构造了置信区间.其次给出不同先验下FW分布参数的满条件分布并证明其为对数凹函数,于是运用Gibbs抽样方法得出参数、可靠度和失效率的Bayes估计和后验可信区间.最后通过数值模拟得出一致的结论,在选取合适的先验时,Bayes结果优于MLE。
[Abstract]:Bebbington et al. (2007) proposed a two-parameter modified Weibull (FW) distribution, which has a simple failure rate function. When given different parameter values, the failure rate can be monotonously increased, or it can be modified bathtub. As a special order statistic, recording value has been widely used in many fields such as reliability analysis because of its important theoretical significance and application value. In this paper, the classical method and Bayes method are used to study the reliability statistical analysis of the distribution. Firstly, the concept, properties and likelihood function of record value are given. Secondly, the properties of FW distribution failure rate are introduced and the theory of WPP graph method is given. Then the FW distribution parameters, regression estimation of reliability and failure rate, inverse moment estimation, MLE and confidence interval based on observation information matrix are discussed, and the corresponding confidence interval is constructed by Bootstrap method. Under the assumption that the two parameter priori is Gamma prior and no information prior, it is proved that the full conditional posterior distribution of FW distribution parameters is logarithmic concave function, so that the Gibbs sampling method can be used to obtain Markov Chain Monte Carlo (MCMC) samples, and the Bayes estimation and posterior confidence interval of parameters, reliability and failure rate can be obtained. Finally, various estimation results are obtained by example simulation, and the mean square error and confidence interval constructed by bootstrapper method and Gibbs sampling method are compared to compare the parameters, regression estimation of reliability and failure rate, inverse moment estimation, MLE and Bayes estimation. The results show that when a suitable priori is selected, Bayes estimation is superior to other estimates, MLE is superior to inverse moment estimation and regression estimation, and the accuracy of regression estimation is the worst, and the confidence interval based on observation information matrix and bootstrapper method is better than that based on observation information matrix. The fourth chapter mainly studies the reliability statistics of FW distribution based on record value samples. Firstly, the MLE, of parameters, reliability and failure rate are given, and the confidence interval is constructed based on the observation information matrix. Secondly, the full conditional distribution of FW distribution parameters under different priori is given and proved to be logarithmic concave function, so the Bayes estimation and posterior confidence interval of parameters, reliability and failure rate are obtained by using Gibbs sampling method. Finally, the consistent conclusion is obtained by numerical simulation. When selecting the appropriate prior, the Bayes result is better than that of MLE..
【学位授予单位】：内蒙古工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O21
本文编号：2502310
[Abstract]:Bebbington et al. (2007) proposed a two-parameter modified Weibull (FW) distribution, which has a simple failure rate function. When given different parameter values, the failure rate can be monotonously increased, or it can be modified bathtub. As a special order statistic, recording value has been widely used in many fields such as reliability analysis because of its important theoretical significance and application value. In this paper, the classical method and Bayes method are used to study the reliability statistical analysis of the distribution. Firstly, the concept, properties and likelihood function of record value are given. Secondly, the properties of FW distribution failure rate are introduced and the theory of WPP graph method is given. Then the FW distribution parameters, regression estimation of reliability and failure rate, inverse moment estimation, MLE and confidence interval based on observation information matrix are discussed, and the corresponding confidence interval is constructed by Bootstrap method. Under the assumption that the two parameter priori is Gamma prior and no information prior, it is proved that the full conditional posterior distribution of FW distribution parameters is logarithmic concave function, so that the Gibbs sampling method can be used to obtain Markov Chain Monte Carlo (MCMC) samples, and the Bayes estimation and posterior confidence interval of parameters, reliability and failure rate can be obtained. Finally, various estimation results are obtained by example simulation, and the mean square error and confidence interval constructed by bootstrapper method and Gibbs sampling method are compared to compare the parameters, regression estimation of reliability and failure rate, inverse moment estimation, MLE and Bayes estimation. The results show that when a suitable priori is selected, Bayes estimation is superior to other estimates, MLE is superior to inverse moment estimation and regression estimation, and the accuracy of regression estimation is the worst, and the confidence interval based on observation information matrix and bootstrapper method is better than that based on observation information matrix. The fourth chapter mainly studies the reliability statistics of FW distribution based on record value samples. Firstly, the MLE, of parameters, reliability and failure rate are given, and the confidence interval is constructed based on the observation information matrix. Secondly, the full conditional distribution of FW distribution parameters under different priori is given and proved to be logarithmic concave function, so the Bayes estimation and posterior confidence interval of parameters, reliability and failure rate are obtained by using Gibbs sampling method. Finally, the consistent conclusion is obtained by numerical simulation. When selecting the appropriate prior, the Bayes result is better than that of MLE..
【学位授予单位】：内蒙古工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O21
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