應用累積暴露模式至單調過程之加速衰變模型

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姓名

張孟筑(Meng-Chu Chang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

應用累積暴露模式至單調過程之加速衰變模型
(Monotonic Process Applied in Accelerated Degradation Tests Based on Cumulative Exposure Model)

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摘要(中)

加速衰變試驗目前已廣泛地被使用，以評估高可靠度產品在正常應力下的壽命資訊。然而加速衰變模型與環境應力之間的關連性中，相關的物理/化學機制和統計意義卻鮮少探討。因此本文考慮加速衰變模型為具隨機效應 (random effects) 之單調過程，以累積暴露 (cumulative exposure) 模式為物理/化學機制，推得模型中參數與加速應力之間的關係式，進而賦予其統計意義。再以常用的逆高斯 (inverse Gaussian) 和伽瑪(gamma) 過程為例，和文獻上常用的加速衰變模型做詳細比較，並提出 EM 演算法估計新加速衰變模型的未知參數。最後，藉由三組實例分析，呈現在不同關係式的假設下，模型配適的差異性、產品壽命推論的精準性、相對應的信賴區間以及加速衰變模型的適合性等。

摘要(英)

Accelerated degradation tests are widely used to assess lifetime information under normal stress for high-reliability products. However, the physical/chemical mechanism as well as the statistical interpretation of the relationship between the accelerated degradation model and the environmental stress is rarely addressed.
In this thesis, we consider accelerated degradation models based on monotonic processes with random effects. By adopting the assumption of cumulative exposure model due to the physical/chemical mechanism, relationships between the model parameters and the acceleration factor are derived which also provide sensible statistical interpretation. Inverse Gaussian and gamma processes are used as examples in which the proposed method is applied and compared with common accelerated degradation models in literature. Expectation-Maximization (EM) algorithm is employed to estimate the unknown parameters of the proposed accelerated degradation model. Finally, three data sets are analyzed to illustrate the performance of the degradation models under different relationships based on the model adequacy, the accuracy of product′s lifetime inference and the corresponding confidence intervals and the goodness of fit.

關鍵字(中)

★ 逆高斯過程
★ 伽瑪過程
★ 隨機效應
★ 加速因子不變原則
★ 拔靴法
★ 覆蓋機率

關鍵字(英)

★ Inverse Gaussian process
★ gamma process
★ random effect
★ acceleration factor constant principle
★ bootstrap
★ coverage probability

論文目次

摘要....................................................i
Abstract...............................................ii
誌謝..................................................iii
目錄...................................................iv
圖目錄.................................................vi
表目錄...............................................viii
1 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
1.4 本文架構...........................................4
2 第二章單調過程之加速衰變模型...........................5
2.1 累積暴露模式.......................................6
2.2 逆高斯過程參數與加速因子之關係式.....................8
2.3 伽瑪過程參數與加速因子之關係式......................13
3 第三章參數估計和信賴區間..............................16
3.1 EM演算法.........................................16
3.1.1 加速衰變模型 M_(μ,λ,1)^IG 之參數估計..........16
3.1.2 加速衰變模型 M_(α,1)^G 之參數估計.............19
3.2 修正偏差百分位拔靴法...............................21
3.2.1 信賴區間.....................................21
3.2.2 覆蓋機率.....................................22
3.3 加速衰變模型之適合度檢定...........................24
4 第四章實例研究.......................................26
4.1 壓力鬆弛資料分析..................................28
4.2 Device-B 資料分析.................................34
4.3 LED 資料分析......................................41
4.4 資料分析之結論....................................49
5 第五章結論與未來研究..................................50
參考文獻................................................51
附錄...................................................55
A. 逆高斯過程參數與加速因子之關係式.....................55
B. 伽瑪過程參數與加速因子之關係式.......................58
C. 逆高斯過程 M_(μ,λ,2)^IG-M_(μ,λ,4)^IG 之對數概似函數.59
D. 伽瑪過程 M_(α,2)^G 之對數概似函數...................60

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指導教授

樊采虹、彭健育(Tsai-Hung Fan Chien-Yu Peng)

審核日期

2017-7-13

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