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研究生：	吳展任 Wu, Chan-Jen
論文名稱：	基於逆高斯過程加速衰變試驗最適實驗設計 Optimal allocation design for accelerated degradation test with inverse Gaussian process
指導教授：	李宜真 Lee, I-Chen
學位類別：	碩士 Master
系所名稱：	管理學院 - 統計學系 Department of Statistics
論文出版年：	2019
畢業學年度：	107
語文別：	英文
論文頁數：	33
中文關鍵詞：	逆高斯過程, 加速衰變試驗、最適實驗設計、V-optimality 、蒙地卡羅重抽樣方法
外文關鍵詞：	inverse Gaussian process, optimum design, accelerated degradation test, V-optimality, Monte-Carlo resampling method
相關次數：	點閱：106 下載：3
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加速衰變試驗分析廣泛地用以推論高可靠度產品的壽命資訊 (如產品壽命第 p 百分位數、平均失效時間)。然而如何規劃一個加速衰變試驗並決定加速應力以及其樣本數，用以推論高可靠度產品壽命資訊是工程師常常遇到的決策問題。目前已經有許多文獻探討最適實驗設計的問題。本研究考慮具隨機效應與固定效應逆高斯過程探討恆定應力加速衰變試驗之最適實驗配置，利用極小化產品正常使用狀況下壽命分位數之變異數為準則求得兩個應力實驗配置下之最適樣本數與最適應力水準之最適實驗配置。我們修正文獻中固定效應逆高斯過程最適實驗設計結果。此外我們探討使用近似分佈或確切分佈對退化衰變路徑壽命分佈之最適實驗配置影響。對於具隨機效應逆高斯過程，我們利用了蒙地卡羅重抽樣方法得到兩應力水準下之最適實驗配置。

Degradation data analysis is widely used to make inference of the lifetime information for high-reliability products (e.g., p−th quantile, mean time to failure). Hence, it is an important issue for engineers to set up an efficient optimum ADT plan. Many literatures discussed this issue of the optimum designs. This study concerns the optimum test plans of constant stress accelerated degradation test with V-optimality for the inverse Gaussian processes with random effects and fixed effects. In this study, we correct results of the optimum design in literature based on the inverse Gaussian process with fixed effect. Furthermore, we explores the effect of optimum designs by using approximate distribution and exact distribution for the lifetime distribution of degradation paths. For the inverse Gaussian process with random effect, we use the Monte-Carlo resampling method to yield an optimum test plans for a two-level ADT.

Table of Contents
摘要 i
Abstract ii 
誌謝 iii 
Table of Contents iv
 List of Tables vi 
List of Figures vii
Chapter 1. 
Introduction and literature review 1
1.1. Introduction.................................. 1 
1.2. Literaturereview ............................... 2 
1.3. Motivation................................... 2 
1.4. Conceptualframework ............................ 3
Chapter 2. IG process with random effect 4
2.1. InverseGaussianprocess ........................... 4 
2.2. InverseGaussianprocesswithrandomeffects . . . . . . . . . . . . . . . . 4 
2.2.1. Randomvolatilitymodel ....................... 5 
2.2.2. Randomdriftmodel.......................... 5 
2.2.3. Randomdriftandrandomvolatilitymodel . . . . . . . . . . . . . . 6
 2.3. Lifetimedistribution ............................. 6 
2.3.1. Exactlifetimedistribution ...................... 6 
2.3.2. The product’s approximation lifetime distribution . . . . . . . . . . 8
Chapter 3. Optimum design 9
3.1. ADTassumptions............................... 9 
3.2. Maximumlikelihoodestimations....................... 10 
3.3. V-optimality.................................. 12
3.3.1. Fisher information matrix- fixed effect model . . . . . . . . . . . . 13
3.3.2. Fisher information matrix - random effect model . . . . . . . . . . 14
3.3.3. Monte Carlo resampling method for computing information matrix . 15
Chapter 4. Illustrative example 17
4.1. Stressrelaxationdata(Yang,2007)...................... 17 
4.1.1. Optimumdesign-fixedeffectmodel(M1) . . . . . . . . . . . . . . 19 
4.1.2. Optimaldesign-randomeffectmodels. . . . . . . . . . . . . . . . 21
4.2. Optimum design with varying parameter for M1 model . . . . . . . . . . . 23
Chapter 5. Concluding remarks and future work 26
5.1. Concludingremarks.............................. 26 
5.2. Futurework.................................. 28
References 29
Appendix A.  Asymptotic variance formula for the fixed effect model 31 
Appendix B.  Optimum design for the random effect model 33

                                    

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校內：2024-07-30公開
校外：2024-07-30公開

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