改进威布尔分布的可靠性统计分析

发布时间：2018-08-07 18:36

【摘要】：改进的威布尔分布(MWD)是在可靠性统计推断中常用的威布尔分布的基础上拓展而来的,它既有威布尔分布具有单调递增失效率这一优点,又弥补了其不具有浴盆形失效率这一弱点.在可靠性分析和寿命试验中,由于试验条件的局限性,寿命试验无法获得全样本观测数据.因此在实际应用中为了节约成本与时间,经常选取截尾样本分析推断寿命分布的总体特征.本文主要讨论基于广义逐次Ⅱ型截尾(GPC-Ⅱ)数据下MWD的参数、可靠度和失效率的极大似然估计以及贝叶斯估计问题.首先介绍了可靠度以及失效率概念及性质并给出详细的证明.其次讨论了基于GPC-Ⅱ数据两参数MWD的极大似然估计和贝叶斯估计,在贝叶斯估计中采用Lindley近似逼近法和MCMC随机模拟法得到参数、可靠度和失效率的贝叶斯估计以及相应的区间估计,并且给出了Lindley近似逼近法的估计精度.然后介绍三参数MWD的极大似然估计以及贝叶斯估计,极大似然估计中采用Fisher观测信息矩阵和Bootstrap法得到相应的置信区间;贝叶斯估计中同时采用M-H抽样法和G-M抽样法得到参数、可靠度和失效率的估计以及相应的区间估计.最后通过数值模拟采用均方误差作为估计精度比较分析各种估计方法的优劣性,结果发现贝叶斯估计在处理小样本时估计精度更高;在MCMC模拟过程中有信息先验下的贝叶斯估计结果优于无信息先验下的贝叶斯估计.数值模拟结果表明G-M抽样法比M-H抽样法抽样效率高;最高后验密度可信区间比渐进正态分布置信区间更为合理;Lindley近似逼近法计算方便但有局限性,MCMC模拟方法需借助计算机数次迭代计算,但是估计精度相对比较高.
[Abstract]:The improved Weibull distribution (MWD) is extended on the basis of the Weibull distribution commonly used in reliability statistical inference. It has the advantages of monotone increasing failure rate. It also compensates its does not have the bathtub shape to lose the rate this one weakness. In reliability analysis and life test, due to the limitation of test conditions, the whole sample observation data can not be obtained by life test. Therefore, in order to save cost and time in practical application, truncated samples are often selected to analyze the overall characteristics of inferred life distribution. In this paper, the parameters, reliability and failure rate maximum likelihood estimation and Bayesian estimation of MWD based on generalized successive type 鈪，

本文编号：2170973