學生-t 過程之破壞性衰變分析

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李侑瑾(Yu-Chin Lee) 查詢紙本館藏

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統計研究所

論文名稱

學生-t 過程之破壞性衰變分析
(Student-t Processes for Destructive Degradation Analysis)

相關論文

★ 串聯系統加速壽命試驗之最佳妥協設計	★ 加速破壞性衰變模型之貝氏適合度檢定
★ 累積暴露模式之單調加速衰變試驗

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至系統瀏覽論文 (2025-9-25以後開放)

摘要(中)

破壞性衰變試驗在量測過程中，產品需經破壞方能取得與壽命相關之品質特徵值，卻無法再測試，導致每個樣本只有一筆衰變資料，提供非常有限的可靠度資訊。而高斯過程被廣泛地應用於衰變分析，但對厚尾資料之配適未臻理想。本文以包含高斯過程之學生-t 過程為基礎，建立具有隨機效應之 (加速) 破壞性衰變模型，期能擬合具厚尾特徵的 (加速) 破壞性衰變資料，進而推論 (在正常應力下) 產品之壽命分配與相關性質。同時以多組實際資料說明產品壽命之可靠度估計、信賴區間以及模型之適合度診斷等。

摘要(英)

In a destructive degradation test, one must destroy the products to obtain values of the quality characteristic. As a result, only one meaningful measurement of the quality characteristic can be taken from each test unit. To analyze the degradation data, Gaussian process is a general model although it is not so appropriate to deal with heavy-tailed data. This thesis proposes a Student-t process, which includes Gaussian process as a special case, to assess the possibly heavy-tailed behavior of the degradation data and to draw the corresponding reliability inferences on the lifetime distribution. Random effects are introduced into the model to address the possible unit-to-unit variation. Five data sets are analyzed by the Student-t process and the resulting reliability analyses of products’ lifetime distributions as well as the goodness-of-fit tests are made based on the models selected via Akaike information criterion.

關鍵字(中)

★ 破壞性衰變試驗
★ 高斯過程
★ 學生-t 過程
★ 厚尾
★ 批次效應

關鍵字(英)

★ destructive degradation test
★ Gaussian process
★ Student-t process
★ heavy-tail
★ batch effects

論文目次

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 本文架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二章破壞性學生 -t 過程之統計推論 5
2.1 廣義學生 -t 過程之破壞性衰變模型 . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 具批次效應之破壞性衰變模型 . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 產品壽命分配 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 參數估計之最大概似法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
第三章 ( 加速 ) 破壞性學生 -t 過程之資料
分析 15
3.1 資料分析流程 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 濃硫酸容器資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 黏著劑 B 黏力資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 黏著劑 K 黏力資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5 聚合物拉力比例資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.6 產品密封強度資料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
第四章結論與未來展望 39
附錄 A 40
參考文獻 42

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指導教授

樊采虹彭健育

審核日期

2020-9-29

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