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研究生: Octavina
Octavina
論文名稱: 相依組件串聯系統的貝氏可靠度分析
Bayesian Reliability Analysis of Series Systems with Dependent Components
指導教授: 林希偉
Shi-Woei Lin
口試委員: 葉瑞徽
Ruey-Huei Yeh
羅士哲
Shih-Che Lo
學位類別: 碩士
Master
系所名稱: 管理學院 - 工業管理系
Department of Industrial Management
論文出版年: 2015
畢業學年度: 103
語文別: 英文
論文頁數: 76
中文關鍵詞: copula整合式分析非整合式分析蒙地卡羅模擬分類樹
外文關鍵詞: copula, aggregate analysis, disaggregate analysis, Monte Carlo simulation, classification tree.
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  • 整合式 (aggregate)與非整合式 (disaggregate) 分析是使用貝氏方法評估系統可靠度時的兩個不同選項。非整合式分析雖然可以提供較精確的估計,但如果相對誤差不大,則僅需系統故障資訊的整合式分析往往因成本較低而在實務上得到青睞。當系統中元件的故障率並非統計獨立時,非整合式分析的複雜程度與運作成本將更為可觀,在實務考量上,除整合式分析外,亦可使用加入獨立性假設的簡易版非整合式分析來估算系統可靠度。本研究的目的在找出影響不同的分析方法之相對誤差的關鍵因子及參數,透過使用 Copula 方法定義並描述元件之間的相依性,使用蒙地卡羅模擬法模擬故障事件的資料,並採用分類樹模型進行重要參數與決策規則的萃取,本研究據此訂出選擇貝氏可靠度分析方法的重要指導原則。


    The system reliability can be evaluated by employing either the aggregate or disaggregate approaches when Bayesian methods are incorporated in the analysis. Even though the aggregate analysis is usually less costly and more practical, disaggregate analysis can provide more accurate results. In practice, the information content at lower level can be forfeited when the magnitude of error between the aggregate and disaggregate analyses is relatively small. Moreover, under similar circumstances, when the components are dependent, a simplified disaggregate analysis without considering the dependence structure might also be used instead of the true disaggregate analysis. Generally, this study aims to identify and locate the exact values of the key factors that produce a great magnitude of error so that a reliable guideline on how to select a proper analysis approach under certain circumstances can be provided. In order to do so, an integrated Monte Carlo simulation and classification tree learning is proposed. Along with that objective, a copula-based Bayesian reliability model together with its theoretical and practical frameworks to model the dependency are delineated in this work.

    摘要 i ABSTRACT ii TABLE OF CONTENTS iii LIST OF FIGURES v LIST OF TABLES vi CHAPTER 1 INTRODUCTION 1 1.1. Background 1 1.2. Problem Definition 3 1.3. Purpose of the Research 3 1.4. Importance of the Research 4 CHAPTER 2 LITERATURE REVIEW 5 2.1. Bayesian Reliability Analysis 5 2.2. Bayesian Aggregation Error 6 2.3. Dealing with Dependency Issue 9 2.4. Key Factors Mapping 10 CHAPTER 3 METHODOLOGY 13 3.1. Developing the Copula-Based Bayesian Reliability Model 13 3.1.1. Simple Series Poisson-Gamma System 13 3.1.2. Aggregate and Disaggregate Analyses 14 3.1.3. Bivariate Copula 15 3.2. Mapping the Key Factors 18 3.2.1. Monte Carlo Filtering and Regionalized Sensitivity Analysis 18 3.2.2. Classification Modeling 21 CHAPTER 4 COPULA-BASED BAYESIAN RELIABILITY 24 4.1. Copula-Based Bayesian Reliability Model 24 4.1.1. Disaggregate Analysis 25 4.1.2. Aggregate Analysis 25 4.1.3. Simplified Disaggregate Analysis 26 4.1.4. General Results 27 4.2. Monte Carlo Simulation Study 30 4.2.1. Separated Scheme Analysis 31 4.2.2. Integrated Scheme Analysis 34 CHAPTER 5 INTEGRATED MONTE CARLO FILTERING AND CLASSIFICATION TREE LEARNING 39 5.1. Imbalanced Data Set 39 5.2. Incorporating Modified Parameters as the Input Factors 42 5.3. Recommendations and Suggestions 49 CHAPTER 6 CONCLUSION 56 REFERENCE 59 APPENDIX 63

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