線性衰退模型之經驗貝氏可靠度分析

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姓名

黃筱涵(Hsiao-han Huang) 查詢紙本館藏

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統計研究所

論文名稱

線性衰退模型之經驗貝氏可靠度分析
(A Empirical Bayesian Reliability Analysis of Linear Degradation Model)

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摘要(中)

本文考慮產品衰退特徵值來自與時間相關的線性模型，在常態模型下，考慮參數具共軛先驗結構，利用貝氏方法可得參數之確切後驗分配，進而提出貝氏可靠度推論；另一方面，由於同款產品之間的衰退模型可能存有個別差異，我們以試驗中觀察到的資料估計具個別差異不同參數模型中但卻有共同先驗分配之超參數，建立經驗貝氏之可靠度推論，處理模型的不確定性。模擬結果顯示當不確定產品的模型時，經驗貝氏方法對於資料分析較具穩健性。

摘要(英)

This thesis considers the degradation data of different products collected via the time-dependent linear models. Exact posterior distributions of the underlying parameters are derived based on the conjugate structure, and Bayesian reliability inference of the failure time distribution is introduced. On the other hand, the degradation models of similar products may have individual differences, empirical Bayes approach is applied by estimating the hyperparameters of the common prior distribution using the observed data via EM algorithm. This approach yields small Bayes predictive risks under model uncertainty. Simulation results show that the empirical Bayes approach is more robust when the model is uncertain or when the prior information is vague.

關鍵字(中)

★ 衰退試驗
★ 線性模型
★ 貝氏方法
★ 經驗貝氏

關鍵字(英)

★ Degradation tests
★ Linear model
★ Bayesian approach
★ Empirical Bayes

論文目次

摘要 i
Abstract ii
誌謝 iii
目錄 v
圖目次 vii
表目次 viii
第一章緒論 1
1.1 研究動機 . ........................................ 1
1.2 文獻探討 . ........................................ 2
1.3 研究方法 . ........................................ 4
第二章線性衰退模型之貝氏推論 5
2.1 線性模型之貝氏推論 . .................................. 5
2.2 線性衰退模型之貝氏推論 . ............................... 6
2.2.1 具個別差異之模型 . ............................... 6
2.2.2 具部分差異之模型 . ............................... 9
2.2.3 不具差異之共同模型 . .............................. 11
2.3 產品失效時間分配 . ................................... 12
第三章經驗貝氏模型 16
3.1 經驗貝氏方法 . ...................................... 16
3.2 EM演算法 . ........................................ 17
第四章模擬研究 22
4.1 具個別差異之模型模擬資料的可靠度分析 . ...................... 22
4.2 具部分差異之模型模擬資料的可靠度分析 . ...................... 28
4.3 不具差異之共同模型模擬資料的可靠度分析 . ..................... 32
4.4 模型比較 . ........................................ 33
4.5 貝氏預測風險 . ...................................... 36
4.6 案例分析 . ........................................ 38
第五章結論與展望 41
參考文獻 42

參考文獻

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指導教授

樊采虹(Tsai-hung Fan)

審核日期

2015-7-27

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