【摘要】：改進的威布爾分布(MWD)是在可靠性統(tǒng)計推斷中常用的威布爾分布的基礎上拓展而來的,它既有威布爾分布具有單調(diào)遞增失效率這一優(yōu)點,又彌補了其不具有浴盆形失效率這一弱點.在可靠性分析和壽命試驗中,由于試驗條件的局限性,壽命試驗無法獲得全樣本觀測數(shù)據(jù).因此在實際應用中為了節(jié)約成本與時間,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以及貝葉斯估計問題.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的極大似然估計和貝葉斯估計,在貝葉斯估計中采用Lindley近似逼近法和MCMC隨機模擬法得到參數(shù)、可靠度和失效率的貝葉斯估計以及相應的區(qū)間估計,并且給出了Lindley近似逼近法的估計精度.然后介紹三參數(shù)MWD的極大似然估計以及貝葉斯估計,極大似然估計中采用Fisher觀測信息矩陣和Bootstrap法得到相應的置信區(qū)間;貝葉斯估計中同時采用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以及相應的區(qū)間估計.最后通過數(shù)值模擬采用均方誤差作為估計精度比較分析各種估計方法的優(yōu)劣性,結(jié)果發(fā)現(xiàn)貝葉斯估計在處理小樣本時估計精度更高;在MCMC模擬過程中有信息先驗下的貝葉斯估計結(jié)果優(yōu)于無信息先驗下的貝葉斯估計.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;最高后驗密度可信區(qū)間比漸進正態(tài)分布置信區(qū)間更為合理;Lindley近似逼近法計算方便但有局限性,MCMC模擬方法需借助計算機數(shù)次迭代計算,但是估計精度相對比較高.
[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：2170973