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研究生： 彭冠榕
Kuan-Jung Peng
論文名稱： 具韋伯壽命分佈之串聯系統在隱蔽資料加速壽命實驗下之可靠度分析
Reliability Analysis of a Series System on Weibull Step-stress Accelerated Life Tests with Masked Data
指導教授： 樊采虹
Tsai-Hung Fan
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 98
語文別： 英文
論文頁數： 48
中文關鍵詞： 加速壽命實驗 、期望值-最大化演算法 、馬可夫鏈蒙地卡羅 、隱蔽資料 、對稱性假設 、有母數拔靴法
外文關鍵詞： accelerated life testing, masked data, symmetry assumption, Markov chain Monte Carlo, EM-algorithm, parametric bootstrap method
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    • 本文主要探討在物件壽命為韋伯分佈之串聯系統的可靠度分析。對高可靠度產品，時常無法在正常環境下蒐集足夠的資料，因此常採用設限階段應力加速實驗。 而在串聯系統中，一般常常只觀察到系統失效的時間，至於真正造成系統失效的物件卻不得而知，只知道可能引起系統失效之物件集合，這樣的資料稱為隱蔽資料。一般常假設隱蔽的發生具對稱性假設，即系統產生隱蔽的機率與物件無關。本文將分別使用貝氏方法與最大概似法在串聯物件壽命具韋伯分佈且其尺度參數與應力具對數線性關係之階段加速實驗下，分別討論在對稱和非對稱線性隱蔽模型下之可靠度分析，其中貝氏方法將以馬可夫鏈蒙地卡羅演算法模擬後驗分佈及其推論，而最大概似法將使用期望值-最大化演算法求其參數之最大概似估計，並以有母數拔靴法估計其標準誤差。最後以模擬研究及闡述舉例來說明所提方法之可行性。

    In this thesis, reliability analysis of a series system consisting of J independent Weibull lifetime components is the main purpose. Due to high reliability product, we can not collect enough data under normal environment. A step-stress accelerated life test is employed for K-stage and M-stress variables under Type-I censoring scheme. In reality, not only the system lifetimes but also the sets containing the possible causes of failure are observed since the failure cause of the system may be lost. Such data are called masked. In general, the symmetry assumption for masking probabilities is assumed. We will consider the scale parameters of the Weibull lifetime distributions of the components is of a log-linear relationship with the stress variables. Bayesian approach via the Markov chain Monte Carlo procedure and the maximum likelihood approach with EM-algorithm and parametric bootstrap method are both developed for reliability analyses of the components as well as the system. Simulation studies and illustrative examples are presented.

    摘要 .....................i Abstract .....................ii 誌謝 .....................iii Table of Contents .....................v List of Figures .....................vii List of Tables .....................viii 1. Introduction .....................1 1.1 Motivation and Background .....................1 1.2 Proposed Methods .....................4 2. Bayesian Approach .....................7 2.1 Model Description and Notation .....................7 2.2 Posterior Inference with Symmetry Assumption .....................10 2.3 Posterior Inference without Symmetry Assumption .....................15 3. Maximum Likelihood Approach .....................19 3.1 MLE with Symmetry Assumption .....................19 3.2 Parametric Bootstrapping of the Standard Errors .....................20 3.3 ML Inference without Symmetry Assumption .....................23 4. Simulation Study .....................25 4.1 Simulation Study with Symmetry Assumption .....................25 4.2 Illustrative Example for ALT Model with Symmetry Assumption .....................31 4.3 Simulation Study without Symmetry Assumption .....................36 4.4 Illustrative Example for ALT Model without Symmetry Assumption .....................39 5. Concluding Remarks .....................43 Reference .....................44

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