加速破壞性衰變模型之貝氏適合度檢定

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姓名

劉哲融(Jhe-rong Liou) 查詢紙本館藏

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統計研究所

論文名稱

加速破壞性衰變模型之貝氏適合度檢定
(Bayesian Goodness-of-Fit Tests for Accelerated Destructive Degradation Models)

相關論文

★ 串聯系統加速壽命試驗之最佳妥協設計	★ 累積暴露模式之單調加速衰變試驗
★ 學生-t 過程之破壞性衰變分析

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摘要(中)

破壞性加速衰變試驗用以評估一次性產品之相關可靠度資訊，其試驗中若欲測量與產品壽命相關品質特徵值，需將產品予以破壞，各測試產品僅有一筆衰變數據。本文考慮具量測誤差混合效應破壞性衰變模型之貝氏可靠度分析，並在貝氏的架構下提出估計虛擬失效時間的方法。以近似衰變分析方法驗證破壞性加速衰變模型所得產品壽命分配之適合性，同時也考慮貝氏適合度檢定下之模型適合度。最後分析五組實際資料，檢視資料中所配適模型之適合度及推論相關可靠度資訊。

摘要(英)

The accelerated destructive degradation tests are used to assess the reliability information of one-shot products. To measured the quality characteristics related to product lifetime, the product needs to be destroyed during the measurement process, and each test unit has only one degradation data. In this thesis, we consider the Bayesian reliability analysis of the destructive degradation model which is mixed-effect model include measurement errors, and propose a method to estimate the pseudo failure time under the Bayesian framework. The approximate degradation analysis method is used to assess goodness-of-fit of the product life distribution which induced by destructive accelerated degradation model, and also consider the model checking under the Bayesian goodness-of-fit test. Finally, five data set are analyzed, Evaluate the adequacy of the model fitted in the data. and infer relevant reliability information.

關鍵字(中)

★ 破壞性加速衰變試驗
★ 適合度檢定
★ 虛擬失效時間
★ 貝氏方法

關鍵字(英)

論文目次

摘要i
Abstract ii
誌謝iii
目錄iv
圖目錄vii
表目錄xii
第一章緒論1
1.1 研究動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻探討 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 研究方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 本文架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 第二章破壞性衰變模型之貝氏可靠度推論7
2.1 具量測誤差破壞性衰變模型之最大概似推論. . . . . . . . . . . . . . . . . 7
2.1.1 具產品間變異性之模型. . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 具批次效應之模型. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
iv
2.2 產品壽命分配與可靠度資訊. . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 貝氏估計與可靠度推論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 貝氏估計 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 貝氏可靠度推論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 第三章破壞性衰變模型之貝氏適合度檢定17
3.1 基於殘差之虛擬失效時間估計 . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 具量測誤差模型之虛擬失效時間 . . . . . . . . . . . . . . . . . . . 17
3.1.2 具批次效應模型之虛擬失效時間 . . . . . . . . . . . . . . . . . . . 18
3.2 貝氏虛擬失效時間之估計 . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 貝氏適合度檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 第四章模擬研究與破壞性衰變資料之實例分析23
4.1 分析步驟 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 模擬資料之分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3 破壞性加速衰變模型實例分析. . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.1 黏著劑 K 黏力資料. . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.2 黏著劑 B 黏力資料. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.3 聚合物拉力比例資料分析. . . . . . . . . . . . . . . . . . . . . . . 53
4.4 破壞性衰變模型之實例分析. . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4.1 濃硫酸容器表厚度資料之分析. . . . . . . . . . . . . . . . . . . . . 62
4.5 具批次效應之破壞性加速衰變模型實例分析. . . . . . . . . . . . . . . . . 70
第五章結論與未來研究87
參考文獻88
v
附錄: 各(加速) 破壞性衰變模型之費雪資訊矩陣92
A.1 黏著劑 K 黏力資料模型之費雪資訊矩陣. . . . . . . . . . . . . . . . . . . 92
A.2黏著劑 B 黏力資料資料模型之費雪資訊矩陣. . . . . . . . . . . . . . . . . . . 94
A.3 聚合物拉力比例資料模型之費雪資訊矩陣. . . . . . . . . . . . . . . . . . 95
A.4 濃硫酸容器表厚度資料模型之費雪資訊矩陣. . . . . . . . . . . . . . . . . 96
A.5 密封強度資料模型之費雪資訊矩陣. . . . . . . . . . . . . . . . . . . . . . 96

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指導教授

樊采虹彭健育

審核日期

2018-8-24

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