逐步應力加速壽命試驗之最佳化問題

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沈冠甫(Kuan-Fu Shen) 查詢紙本館藏

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論文名稱

逐步應力加速壽命試驗之最佳化問題
(OPTIMAL STEP-STRESS ACCELERATED LIFE TESTPLANS WITH PROGRESSIVE CENSORING)

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摘要(中)

由於科技發達在生產技術進步與製造的嚴格控管，產品可靠度不斷提昇;所以對於高可靠度的產品組件，如果在正常使用狀況下，檢驗其壽命分配，或估計其可靠度，往往會費時過久，因此加速壽命試驗(Accelerated Life Testing，ALT)就是在異於正常的使用環境之下，加速產品的失效再推導出產品在正常使用狀況下的壽命。傳統的壽命試驗，常採用型I或型II設限計畫，而這兩種設限計畫皆不允許在試驗中移除未失效之產品，而實務上有時候必須於試驗中，移除部分的未失效產品;因此逐步設限（Progressively censored）便可用來處理這類的問題。因此本篇論文主要在討論逐步應力加速壽命試驗之最佳化問題，我們對貝氏分析以及逐步設限兩種蒐集資料的方式有興趣，在log-linear的模型中，討論這些問題。
本文以階段應力做為加速失效因子，在加速失效模型下，第一部分提出決定主觀或客觀先驗分佈，以得到產品可靠度貝氏推論，決定最適佳階段應力試驗時間與比例的方法。第二部分介紹最佳階段應力在逐步設限狀態下之加速應力壽命試驗計畫，比較型I與型II逐步設限計畫的異同。本文將逐步設限與加速試驗結合在一起，提出逐步設限加速應力壽命試驗計畫，並探討在產品壽命為指數分配時，有關的模型參數估計。並提出決定最適佳階段應力試驗時間與比例的方法，分別是變異數(Variance) V-準則及行列式(Determinant) D-準則。最後舉例做數值上的模擬與分析決定選擇應力與應力間最佳的改變時間及比例。

摘要(英)

First, this paper presents optimum plans for step-stress tests from a Bayes viewpoint. We obtain the optimum test plans to minimize the asymptotic variance of the maximum likelihood estimator of the mean life at a design (use) stress. The emphasis of this paper is to establishment of new areas of application to step-stress accelerated life testing (ALT) and an improvement of existing procedures and theories. Examples for Type I and Type II censored cases are illustrated.
Second, this paper considers the analysis of exponentially distributed lifetime data observed under -stage step-stress accelerated life test with progressive type-I and type-II censoring. Furthermore, the random removal is also discussed and we suppose the number of units removed at each stress follows a binomial distribution. We compute the expected Fisher information matrix of the maximum likelihood estimator of the log mean life at design (use) stress. The problem of choosing the optimal time and proportion under k-stage step-stress is addressed using variance (V)-optimality as well as determinant (D)-optimality criteria. An illustrative example is provided with discussion.

關鍵字(中)

★ 貝氏推論
★ 先驗分佈
★ 後驗分佈
★ 行列式(Determinant) D-準則
★ 變異數(Variance) V-準則
★ 漸近變異數
★ 階段應力
★ 訊息矩陣
★ 逐步設限

關鍵字(英)

★ accelerated life testing
★ progressive censoring
★ asymptotic variance
★ determinant (D)-optimality
★ step-stress
★ variance (V)-optimality

論文目次

第一章緒論……………………………………………………………………………..1
1-1 研究動機與目的………………………………………………………..1
1-2 文獻探討………………………………………………………………..2
1-3 本文架構………………………………………………………………..3
第二章實驗進行程序，模型基本假設及相關符號…………………………………..4
2-1 實驗進行程序…………………………………………………………..4
2-2 模型基本假設…………………………………………………………..5
2-3 相關符號………………………………………………………………..6
第三章貝氏型I、型II設限之階段加壓最佳壽命測試計畫……………………….7
3-1　貝氏二階段型I、型II設限加速試驗之統計模型……….…………7
3-1-1 貝氏二階段型I設限加速試驗之統計模型…………………..7
3-1-2 貝氏二階段型II設限加速試驗之統計模型……….………..11
3-1-3 實例模擬研究…………………………………………………..13
3-2　貝氏三階段型I、型II設限加速試驗之統計模型……………………15
3-2-1 貝氏三階段型I設限加速試驗之統計模型……………..……15
3-2-2 貝氏三階段型II設限加速試驗之統計模型……………..…..20
3-2-3 實例模擬研究…………………………………………………..22
第四章逐歩型I、型II 設限固定移除之階段加壓最佳壽命測試計畫………………25
4-1 逐歩型I 設限固定移除之統計模型……….…………………………..25
4-1-1 逐步型I 設限固定移除加速壽命試驗………………………..25
4-1-2 最適階段試驗時間……………………………………………..28
4-1-3 實例模擬研究…………………………………………………..30
4-2 逐歩型II 設限固定移除之統計模型……….…………………….…..31
4-2-1 逐步設限型II 固定移除加速壽命試驗……………..………..31
4-2-2 最適階段試驗比例……………………………………………..34
4-2-3 實例模擬研究…………………………………………………..36
第五章逐歩型I、型II 設限隨機移除之階段加壓最佳壽命測試計畫……………..38
5-1 逐歩型I 設限隨機移除之統計模型………………………………….. 38
5-1-1 逐步型I 設限隨機移除加速壽命試驗……………………….. 38
5-1-2 最適階段試驗時間……………………………………………..42
5-1-3 實例模擬研究…………………………………………………..44
5-2 逐歩型II 設限隨機移除之統計模型……………………….………...45
5-2-1 逐步設限型II 隨機移除加速壽命試驗……………..………..45
5-2-2 最適階段試驗比例……………………………………………...48
5-2-3 實例模擬研究……………………………………………..…..50
第六章結論………………………………………………………………….………….52
參考文獻、………………………………………………………………………………..53
附錄一、nelson 表……………………………………………………..………………..54
附錄二、貝氏二階段推導公式…………………………………………………………..55
附錄三、貝氏三階段推導公式…………………………………………………………..56

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指導教授

呂理裕(Lii-Yuh Leu)

審核日期

2007-5-22

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