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研究生：	吳孟芳 Wu, Meng-Fang
論文名稱：	退化量測資料之適合度檢定比較 Comparing GOF Tests for Degradation Measurements
指導教授：	鄭順林 Jeng, Shuen-Lin
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：	2018
畢業學年度：	106
語文別：	英文
論文頁數：	67
中文關鍵詞：	計畫性退化量測值、混合型模型、適合度、隨機係數模型、隨機過程、混合型Poisson過程、模型比較
外文關鍵詞：	scheduled degradation measurements, mixture model, Goodness-of-fit (GOF), random coefficient model, stochastic process, compound Poisson process, model-checking
相關次數：	點閱：168 下載：16
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在短期實驗中，提供產品的生命週期評估在可靠性研究中越來越重要，尤其是對於有些產品的退化特徵只能在特定的時間點被觀察。因此，我們對計畫性量測資料去配適兩種類型的退化模型，並使用適合度(goodness-of-fit, GOF) 檢定去評估這兩種模型的適合度。GOF 檢定方法不僅有Anderson-Darling (AD) 檢定，還包括Cramér–von Mises (CM) 和Kolmogorov–Smirnov (KS) 檢定。值得注意的是，GOF 檢定用於累積退化量的分佈。我們考慮在不同的樣本數、參數、模型假設之情況下進行了兩次的模擬研究，其中兩個模擬研究是(1) 雷射數據研究(2) 等變異研究。第一種模型假設是：虛無假設為隨機係數模型，對立假設為隨機過程模型；而第二種模型是：虛無假設為隨機過程模型，對立假設為隨機係數模型。經由模擬研究比較的結果，在虛無假設為隨機係數模型且對立假設為隨機過程模型時，一般而言AD 檢定力通常比其他檢定更高。

Scheduled degradation measurements which provide life cycle assessment of products during the short experiments are increasingly important in reliability studies, especially for the product characteristics of degradation quantities that can only be observed at specific planning time points. We performed a comparison of goodness-of-fit (GOF) tests for two types of degradation models with scheduled measurements. The GOF test methods include not only Anderson-Darling (AD) test but also Cramér–von Mises (CM) and Kolmogorov–Smirnov (KS) test. It’s worth noting that the GOF tests are for the distribution of cumulative degradation values. We conduct two simulation studies under several cases of sample sizes and parameters, where the two simulation studies are (1) laser data study (2) equal variance study. The power comparisons demonstrate that the Anderson-Darling test is generally more powerful for a null random coefficient model against alternative stochastic process model than other tests.

摘要i
Abstract ii
Acknowledgements iii
Table of Contents iv
List of Tables vi
List of Figures vii
Chapter 1. Introduction 1
1.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1. Degradation models . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2. Goodness-of-fit (GOF) tests . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 2. Methodology 7
2.1. Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2. GOF tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1. GOF test statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2. CDF of GOF test statistics . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3. Type I error and power . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3. Likelihood function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1. Random coefficient path model . . . . . . . . . . . . . . . . . . . . 18
2.3.2. Stochastic process model . . . . . . . . . . . . . . . . . . . . . . . . 19
Chapter 3. Simulation study for laser data example 21
3.1. Comparisons of a GOF test at different observation time points . . . . . . 23
3.2. Comparisons of GOF tests at each observation time point . . . . . . . . . 26
Chapter 4. Simulation study for equal variance example 30
4.1. Settings of simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2. Comparisons of a GOF test at different observation time points . . . . . . 32
4.3. Comparisons of GOF tests at each observation time point . . . . . . . . . 35
Chapter 5. Explored topics and future work 37
5.1. Explored topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.1.1. Compound Poisson process . . . . . . . . . . . . . . . . . . . . . . 40
5.1.2. Random coefficient path model and stochastic process model . . 43
5.1.3. Likelihood function of the mixed model . . . . . . . . . . . . . . . 49
5.1.4. Sensibility analysis of parameter setting under supposed model . 50
5.1.5. GOF with parameters unknown . . . . . . . . . . . . . . . . . . . . 52
5.2. Major accomplishments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3. Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
References 58
Appendix A. Model comparison plot 61
Appendix B. Power plot with linear trend model 64
Appendix C. CDFs plot of GOF test with parameter unknown 67
                                    

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校內：2021-08-01公開
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