群組資料指數分配加速壽命試驗之貝氏可靠度分析與最佳化設計

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吳秉懌(Bing-Yi Wu) 查詢紙本館藏

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統計研究所

論文名稱

群組資料指數分配加速壽命試驗之貝氏可靠度分析與最佳化設計

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摘要(中)

在可靠度分析裡，加速壽命試驗是藉由將物件置於較正常環境嚴厲的應力水準下，來減少試驗時間的一種方法；而階段加速壽命試驗則是將同一批物件置於逐漸增加的應力水準下的加速試驗。不同的設限計畫也常被應用在加速壽命試驗，而在壽命試驗中資料又可分為紀錄各物件失效時間的完整資料與只觀測失效的個數群組資料兩種。本文討論資料來自壽命分配為指數分配、單一應力、群集資料下的逐步型I 設限階段加速壽命試驗之最大概似與貝氏推論。由於在可靠度試驗中通常樣本數較少，使得傳統上基於大樣本漸近結果的最大概似推論不甚準確，但貝氏方法卻可在小樣本時提供較穩定的估計。另外，將根據 V-準則、D-準則與 A-準則，分別決定最佳的試驗時間與最佳的階段應力增量。

摘要(英)

Accelarated life test (ALT) is a widely used technique to reduce the experiment time. Experimenters abridge the time by placing the items at the more severe stress levels than at nomal-use contidion. Besides, in the step-stress ALT, the stress levels are gradually increasing. Also, censoring scheme is often applied when the life test is to be executed. Complete data, which record all failure times and grouped data, which only include the numbers of failure items are two types of data in life test. In this thesis, assume that the lifetime of each item follows an exponential
distribution under the single stress progressive Type-I censoring ALT with grouped data. Maximum likelihood as well as Bayesian inferences on the related parameters are developed. The traditional MLE according as the large sample properties is not precise enough since there is no large sample in reliability test. However Bayesian method would offer stable estimation when the sample size is not large. Futhermore, the search for optimal experiment time and optimal stress increment is derived, which is based on V-optimality, D-optiamlity and A-optimality.

關鍵字(中)

★ 型 I 逐步設限
★ 最佳化設計
★ 貝氏分析
★ 加速壽命試驗
★ 群組資料

關鍵字(英)

★ optimal test
★ Type-I progressive censoring
★ Bayesian analysis
★ accelarated life test
★ grouped data

論文目次

中文摘要i
英文摘要ii
致謝辭iii
1 緒論1
1.1 研究動機
1.2 文獻回顧
1.3 研究方法
2 型I 逐步設限階段應力加速壽命試驗推論與最佳設計7
2.1 模型介紹與統計推論
2.1.1 最大概似估計
2.1.2 貝氏推論
2.2 最佳化準則
2.2.1 V-最佳化準則
2.2.2 D-最佳化準則
2.2.3 A-最佳化準則
3 數值分析與模擬研究
3.1 最佳化試驗時間
3.2 最佳化應力增量
3.3 模擬資料研究
4 結論與展望
參考文獻

參考文獻

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指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2008-7-6

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