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研究生： 陳俑輝
Tan, Yung-Hui
論文名稱： 比較在離散退化模型下的三種適合度檢定
Comparing Three GOF Tests for Discrete Degradation Models
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： 2019
畢業學年度： 107
語文別： 英文
論文頁數： 127
中文關鍵詞： 檢定力 、適合度檢定 、退化模型 、非均質性泊鬆過程
外文關鍵詞： Power, GOF Tests, Degradation Model, Non-homogeneous Compound Poisson
相關次數： 點閱：134  下載：4 
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    • 本研究的目的是比較兩種離散退化模型的適合度檢定（GOF）的檢定力。我們探討將特定模型作為虛無假設或對立假設時各種適合度檢定的的檢定力。我們使用來自設備可靠性和軟件可靠性實驗的兩個實際數據集來說明比較過程。我們在指定的假設設置下構建不同樣本大小和時間點的模擬。考慮的三個適合度檢定是Watson 檢定，Cramér-von Mises（CM）檢定，Anderson-Darling（AD）檢定。這項研究的有趣發現是適合度檢定的檢定力會受到假設設置的影響。

    The purpose of this study is to compare the powers of the Goodness-of-fit (GOF) tests for two kinds of discrete degradation models. We explore the powers of the GOF tests for the cases that the specified model is placed as the null hypothesis or as the alternative hypothesis. We use two real data sets from device reliability and software reliability experiment to illustrate the process of the comparisons. We construct simulations for different sample sizes and time points under specified hypothesis setting. The three GOF tests considered are Watson test, Cramér–von Mises (CM) test, Anderson-Darling (AD) test. The interesting discovery
    of this study is that the power of GOF tests depends on the hypothesis settings.

    摘要 i Abstract ii 誌謝 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1. Goodness-of-fit (GOF) Tests . . . . . . . . . . . . . . . . . . . . . 5 1.2.2. Degradation Models . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3. Content of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 2. Methodology 10 2.1. GOF Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1. Type I Error Rate and Power . . . . . . . . . . . . . . . . . . . . . 10 2.1.2. GOF Test Statistics for Continuous Data . . . . . . . . . . . . . . . 12 2.1.3. GOF Test Statistics for Discrete Data . . . . . . . . . . . . . . . . . 13 2.1.4. Discussion of GOF Test Statistic . . . . . . . . . . . . . . . . . . . 15 2.2. Degradation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.1. Nonhomogeneous Continuous-Compound Poisson Model . . . . . . 16 2.2.2. Likelihood Function of NHCCP Model Parameters . . . . . . . . . 18 2.2.3. Nonhomogeneous Discrete-Compound Poisson Model . . . . . . . 22 2.2.4. Likelihood Function of NHDCP Model Parameters . . . . . . . . . 25 2.3. Flow Chart of GOF Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Chapter 3. Simulation Study Based on Real Data 28 3.1. NHCCP Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.1.1. MLEs of NHCCP Models . . . . . . . . . . . . . . . . . . . . . . . 29 3.1.2. Testing for NHCCP Models . . . . . . . . . . . . . . . . . . . . . . 30 3.2. NHDCP Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.1. MLEs of NHDCP Model . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.2. Testing for NHDCP Models . . . . . . . . . . . . . . . . . . . . . 42 3.3. Discussion of Low Power . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Chapter 4. Simulation Study Based on NHCCP Model 46 4.1. Simulation Data from MCL . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.1.1. Setting of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.1.2. Testing of Simulation Data . . . . . . . . . . . . . . . . . . . . . . 48 4.2. Simulation Data from MCW . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.1. Setting of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.2. Testing of Simulation Data . . . . . . . . . . . . . . . . . . . . . . 52 4.3. Simulation Data from MCG . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.3.1. Setting of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.3.2. Testing of Simulation Data . . . . . . . . . . . . . . . . . . . . . . 55 4.4. Discussion of Simulation Result . . . . . . . . . . . . . . . . . . . . . . . 56 Chapter 5. Simulation Study Based on NHDCP Model 57 5.1. Simulation Data from MDB . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1. Setting of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.2. Testing of Simulation Data . . . . . . . . . . . . . . . . . . . . . . 59 5.2. Simulation Data from MDP . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2.1. Setting of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2.2. Testing of Simulation Data . . . . . . . . . . . . . . . . . . . . . . 70 5.3. Discussion of Simulation Result . . . . . . . . . . . . . . . . . . . . . . . 79 Chapter 6. Conclusion and Future Work 80 6.1. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.2. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 References 82 Appendix A. CDFs of GOF Tests Referred to Figure 3.1 84 Appendix B. CDFs of GOF Tests Referred to Figure 3.2 90 Appendix C. CDFs of GOF Tests Referred to Figure 3.3 96 Appendix D. CDFs of GOF Tests Referred to Figure 3.4 102 Appendix E. Type I Error Rates and Powers Referred to Figure 5.5-5.6 108 Appendix F. Type I Error Rates and Powers Referred to Figure 5.11-5.12 118

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