逐步加速壽命試驗之貝氏可靠度分析與最佳化設計

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林章權(Jhang-cyuan Lin) 查詢紙本館藏

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統計研究所

論文名稱

逐步加速壽命試驗之貝氏可靠度分析與最佳化設計
(Bayesian Analysis and Optimal Design in Accelerated Life Tests with Progressively censored Data)

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摘要(中)

加速壽命試驗 (Accelerated Life Testing) 是在異於正常的使用環境下，加速產品的失效以利收集資料，再推導出產品在正常使用狀況下的壽命。本篇論文主要討論在型I與型II逐步設限計畫下應力加速壽命試驗之統計推論及最佳化實驗設計問題。假設產品壽命為指數分配且平均壽命與應力具對數線性關係之模型，我們使用最大概似法和貝氏分析(Bayesian analysis)探討可靠度分析，結果顯示即使在主觀性弱的先驗分佈訊息下仍有助於參數之統計推論。另外並提出在型I逐步設限計畫下階段應力試驗時間與等階段應力增量的最佳設計，同時在型II逐步設限計畫下探討每一階段最佳試驗比例的改變點。此外，也提出在型II逐步設限計畫下同時對試驗時間和參數估計變異數的最佳化準則。最後並以數值模擬做驗證與比較。

摘要(英)

Accelerated life testing of products is used to get information quickly on their lifetime distribution. In this thesis, we discuss k-stage step-stress accelerated life-tests under the progressively Type-I and Type-II censoring schemes, respectively. An exponential lifetime distribution with mean life time that is a log-linear function of the stress variable is considered. The classical maximum likelihood method as well as a fully Bayesian method based on the Markov chain Monte Carlo (MCMC) technique are developed for inference on all the related parameters. From empirical studies, it shows that the Bayesian methodology is quite accurate in drawing inference even in the case of noninformative prior. Under the equi-spaced stress experiment, the optimal stress increment and equal time duration are investigated for Type-I censored data, whereas the optimal sampling plan is discussed under Type-II censoring scheme together with a criterion based on minimizing the expected experimental time and variance of the maximum likelihood estimator simultaneously. Numerical examples are presented for illustration.

關鍵字(中)

★ 貝氏分析
★ 型II逐步設限計畫
★ 型I逐步設限計畫
★ 加速壽命試驗

關鍵字(英)

★ Bayesian method
★ Progressively Type-II censoring scheme
★ Progressively Type-I censoring scheme
★ Accelerated life testing

論文目次

1 Introduction
1.1 Motivation and Background
1.2 Literature Review
1.3 Overview
2 Model Description and Assumptions
2.1 Progressively Type-I Censoring Scheme
2.1.1 ML Inference Under Type-I Censoring Scheme
2.1.2 Progressive Censoring in Small Samples
2.1.3 Bayesian Inference Under Type-I Censoring Scheme
2.1.4 The Jeffreys Prior
2.2 Progressively Type-II Censoring Scheme
2.2.1 Statistical Inference Under Type-II
Censoring Scheme
3 Optimal Designs of Accelerated Lifetime Test
3.1 Type-I Censoring Scheme
3.1.1 Variance-Optimality
3.1.2 D-Optimality
3.1.3 Numerical Illustrations
3.1.4 A-Optimality
3.1.5 Minimax Optimality
3.2 Type-II Censoring Scheme
3.2.1 Variance-optimality, D-optimality and A-optimality
4 Numerical Illustration
4.1 Statistical Inference on the Simulation Data in Type- I ALT
4.2 Optimal Design on the Simulation Data
4.3 Statistical Inference on the Simulation Data in Type- II ALT
5 Concluding Remarks

參考文獻

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指導教授

樊采虹(Tsai-hung Fan)

審核日期

2008-6-26

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