發(fā)布時(shí)間：2018-08-07 18:36

【摘要】：改進(jìn)的威布爾分布(MWD)是在可靠性統(tǒng)計(jì)推斷中常用的威布爾分布的基礎(chǔ)上拓展而來(lái)的,它既有威布爾分布具有單調(diào)遞增失效率這一優(yōu)點(diǎn),又彌補(bǔ)了其不具有浴盆形失效率這一弱點(diǎn).在可靠性分析和壽命試驗(yàn)中,由于試驗(yàn)條件的局限性,壽命試驗(yàn)無(wú)法獲得全樣本觀測(cè)數(shù)據(jù).因此在實(shí)際應(yīng)用中為了節(jié)約成本與時(shí)間,經(jīng)常選取截尾樣本分析推斷壽命分布的總體特征.本文主要討論基于廣義逐次Ⅱ型截尾(GPC-Ⅱ)數(shù)據(jù)下MWD的參數(shù)、可靠度和失效率的極大似然估計(jì)以及貝葉斯估計(jì)問(wèn)題.首先介紹了可靠度以及失效率概念及性質(zhì)并給出詳細(xì)的證明.其次討論了基于GPC-Ⅱ數(shù)據(jù)兩參數(shù)MWD的極大似然估計(jì)和貝葉斯估計(jì),在貝葉斯估計(jì)中采用Lindley近似逼近法和MCMC隨機(jī)模擬法得到參數(shù)、可靠度和失效率的貝葉斯估計(jì)以及相應(yīng)的區(qū)間估計(jì),并且給出了Lindley近似逼近法的估計(jì)精度.然后介紹三參數(shù)MWD的極大似然估計(jì)以及貝葉斯估計(jì),極大似然估計(jì)中采用Fisher觀測(cè)信息矩陣和Bootstrap法得到相應(yīng)的置信區(qū)間;貝葉斯估計(jì)中同時(shí)采用M-H抽樣法和G-M抽樣法得到參數(shù)、可靠度和失效率的估計(jì)以及相應(yīng)的區(qū)間估計(jì).最后通過(guò)數(shù)值模擬采用均方誤差作為估計(jì)精度比較分析各種估計(jì)方法的優(yōu)劣性,結(jié)果發(fā)現(xiàn)貝葉斯估計(jì)在處理小樣本時(shí)估計(jì)精度更高;在MCMC模擬過(guò)程中有信息先驗(yàn)下的貝葉斯估計(jì)結(jié)果優(yōu)于無(wú)信息先驗(yàn)下的貝葉斯估計(jì).數(shù)值模擬結(jié)果表明G-M抽樣法比M-H抽樣法抽樣效率高;最高后驗(yàn)密度可信區(qū)間比漸進(jìn)正態(tài)分布置信區(qū)間更為合理;Lindley近似逼近法計(jì)算方便但有局限性,MCMC模擬方法需借助計(jì)算機(jī)數(shù)次迭代計(jì)算,但是估計(jì)精度相對(duì)比較高.
[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，

本文編號(hào)：2170973