具Marshall-Olkin 二元指數分佈之混合設限競爭風險資料之可靠度分析

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林香漢(Hsiang-han Lin) 查詢紙本館藏

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統計研究所

論文名稱

具Marshall-Olkin 二元指數分佈之混合設限競爭風險資料之可靠度分析
(Competing Risks Model of Marshall-Olkin Bivariate Exponential Distribution Under Hybrid Censoring)

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摘要(中)

在競爭風險模型中, 該物件中的任何一個風險因子失效皆會導致物件失效。由於這些因子來自於同一個物件, 所以因子間可能是相關的。在本篇文章中, 我們考慮在混合設限計劃下, 風險因子具二元Marshall-Olkin 指數壽命的競爭風險模型。混合設限計劃綜合了型一和型二設限計劃, 是壽命試驗或可靠度分析中常用的方法。而在競爭風險模型中, 時常無法得知引起物件失效之風險因子, 這類資料稱為隱蔽資料。我們使用期望值-最大化演算法去求得模型中參數之最大概似估計, 並以遺失資訊法則估計其標準誤。另外我們也分別使用使用主觀先驗分佈和無訊息先驗分佈, 由馬可夫鏈蒙地卡羅方法得貝氏估計。並比較兩種方法所得模型參數以及物件和風險因子的平均壽命和可靠度之統計推論。模擬結果顯示, 當隱蔽資料比率較高時, 資料沒有辦法提供充分的訊息, 但貝氏方法配合可靠的先驗分佈, 所得結果會優於最大概似方法。

摘要(英)

In a competing risks model, the component fails if any of the risk factors fails. These factors are all from the same component, hence they may be correlated. In this thesis, we consider the competing risks model under bivariate Marshall-Olkin exponential distribution under hybrid censoring which is the mixture of conventional Type I and Type II censoring schemes and is quite useful in lifetesting or reliability experiments. It is often to include masked data in which the risk factor that causes failure of the component is not observed. We apply the maximum likelihood approach via EM algorithm along with the missing information principle to estimate the standard errors of the MLE. Bayesian approach incorporated with subjective prior and noninformative prior is also considered with the aid of MCMC method. Statistical
inference on the model parameters as well as the mean lifetimes and the reliability functions of the component and risk factors is derived. Simulation study shows that the maximum likelihood approach performs poorly when the proportion of the masking data is high due to insufficient information, while Bayesian method can be provide good results with reliable prior information.

關鍵字(中)

★ 混合設限計劃
★ 風險競爭模型
★ 隱蔽資料
★ 期望值-最大化演算法
★ 遺失訊息法則
★ 馬可夫鏈蒙地卡羅方法

關鍵字(英)

★ competing risk model
★ hybrid censoring scheme
★ m

論文目次

摘要i
Abstract ii
誌謝iii
Table of Contents iv
List of Figures vi
List of Tables vii
1. Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Proposed Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Statistical Model and the Maximum Likelihood Inference 8
2.1 The Marshall-Olkin Bivariate Exponential Distribution . . . . . . . . . . . . . . 8
2.2 The Competing Risks Model Life Test Under Hybrid Censoring . . . . . . . . . . 10
2.3 Maximum Likelihood Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Fisher Information Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Reliability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3. Bayesian Analysis 24
3.1 Posterior Inference with Noninformative Prior . . . . . . . . . . . . . . . . . . . 24
3.2 Subjective Prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Reliability Analysis for Bayesian . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4. Simulation Study 30
4.1 Simulation Study for Case I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Simulation Study for Case II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Simulation Study under Hybrid Censoring . . . . . . . . . . . . . . . . . . . . . 46
4.4 Illustrative Example for Hybrid Censoring Case . . . . . . . . . . . . . . . . . . 51
5. Concluding Remarks 54
Reference 55

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指導教授

樊采虹(Tsai-hung Fan)

審核日期

2012-6-28

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