串聯系統元件壽命服從韋伯分配下之定應力破壞性加速壽命試驗分析

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蘇瓔漪(Ying-Yi Su) 查詢紙本館藏

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統計研究所

論文名稱

串聯系統元件壽命服從韋伯分配下之定應力破壞性加速壽命試驗分析
(Constant Stress Accelerated Life Tests forDestructive Device of Series Components under Weibull Lifetime Distributions)

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摘要(中)

本文考慮物件壽命為獨立韋伯分配的串聯系統之定應力加速壽命試驗, 其中韋伯分配之尺
度參數和應力變數水準具對數線性關係。首先, 我們考慮在型I 設限下之三物件串聯系統
的完全資料模型, 即觀測資料為系統之失效時間, 但是其中引起系統失效的物件不一定可
被觀察到。若該物件無法被觀察到, 稱此資料為隱蔽資料。我們進一步的將模型推廣到破
壞性元件之串聯系統中, 在給定應力水準下, 我們在特定時間測試每個串聯元件, 觀察在該
時間時, 元件是否仍在正常運作中, 因此觀察到的資料為群集資料和可能引起失效的物件。
當資料被隱蔽時, 我們以期望值-最大化演算法和拔靴法去做最大概似法之推論。另外, 我
們也使用貝氏推論, 其中先驗分配來自關於可靠度之主觀先驗資訊。模擬結果顯示在資料
大部份被隱蔽時, 貝氏分析之結果優於最大概似法。

摘要(英)

In this thesis, we consider modeling the constant stress accelerated life test of a series system
with independent Weibull lifetime components whose scale parameters are log-linear in the
levels of the stress variable. We first consider a three-component series system where the
system lifetime is collected under Type I censoring but the component that causes the system
to fail may or may not be observed. The data are so called masked for the latter case. We
then extend the model to the destructive (also called by one-shot) device of series components
where each device is tested at specific time under given stress level. The data observed are
interval data for the device systems with the associated failed components if observed. When
the data are masked, EM algorithm and the bootstrap method are used to draw the maximum
likelihood inference. Bayesian approach incorporated with subjective priors on the reliability
is also applied. Simulation study shows that Bayesian analysis outperforms the maximum
likelihood approach especially when the data are highly masked.

關鍵字(中)

★ 定應力加速壽命試驗
★ 串聯系統
★ 破壞性元件
★ 韋伯分佈
★ 貝氏方法

關鍵字(英)

★ constant stress ALT
★ series system
★ destructive device
★ Weibull distribution
★ Bayesian approach.

論文目次

摘要i
Abstract ii
誌謝iii
Table of Contents iv
List of Figures vi
List of Tables vii
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Proposed Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 2
Complete Data under Constant Stress ALT 9
2.1 Model Description and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Maximum Likelihood Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Bayesian Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Chapter 3
Destructive Devices under Constant Stress ALT 24
3.1 Maximum Likelihood Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 The normal prior distribution . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.2 The beta prior distribution . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.3 Posterior distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Chapter 4 Simulation Study 35
4.1 Simulation Study with Complete Data . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Simulation Study with Destructive Device . . . . . . . . . . . . . . . . . . . . . 46
Chapter 5 Conclusion 52
Reference 53

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指導教授

樊采虹(Tsai-hung Fan)

審核日期

2012-6-26

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