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研究生: Muhammad Fakhri Alam
Muhammad Fakhri Alam
論文名稱: 串並聯系統貝氏整合誤差之比較分析
Comparative Analysis of Bayesian Aggregation Error in Series and Parallel Systems
指導教授: 林希偉
Shi-Woei Lin
口試委員: 彭奕農
Pong-Yi Nong
陳志萍
Chen-Zhi Ping
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: 2024
畢業學年度: 112
語文別: 英文
論文頁數: 69
中文關鍵詞: 貝氏整合誤差貝氏可靠度模型串聯系統並聯系統copula整合式分 析拆解式分析分類樹
外文關鍵詞: Bayesian aggregation error, Bayesian reliability model, series system, parallel system, copula, aggregate analysis , disaggregate analysis, classification tree
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  • 本論文運用基於copula 的貝氏可靠性模型,探討及比較串聯和並聯系統中,選擇整合式分析(AA)、拆解式分析(DA)以及帶有獨立性假設的拆解式分析(DAI)進行可靠度分析時將如何影響貝氏整合誤差。AA以系統級數據為依據,提供了對系統可靠性的全面概述,但可能忽略了元件之間的重要相依關係;反之,DA納入了關鍵的元件層級數據,有助於理解系統內微妙的交互作用,但運算複雜且耗費資源;DAI可假定元件之間互相獨立來簡化DA 的運算,然現實系統中這種過強的假設往往不成立。本研究針對串聯與並聯系統中影響整合誤差的關鍵因素進行分類和定義,並且界定它們的?值。針對貝氏整合誤差,研究亦透過模擬數據和分類樹,系統性地指出串聯和並聯系統展現相似或不同行為的關鍵條件。


    This thesis employs a copula-based Bayesian reliability model to addresses the issue of choosing among aggregate analysis (AA), disaggregate analysis (DA), and disaggregate analysis with independence assumption (DAI) to mitigate the impact of Bayesian aggregation errors, particularly those that manifest in series and parallel systems. AA, relying on system-level data, provides an overview of system reliability but may overlook component interactions. In contrast, DA incorporates critical component-level data, facilitating an understanding of the subtle interactions within a system but can be resource-intensive and complex. DAI simplifies DA by assuming component independence, yet this assumption may not universally hold, especially in systems with complex dependencies. This research classifies and defines key factors, as well as their threshold values, that distinguish between series and parallel systems in terms of how they respond to errors. In particular, simulated data and classification tree analysis were employed to systematically identify the conditions under which series and parallel systems exhibit similar or divergent behaviors in the presence of Bayesian aggregation errors.

    摘要 i ABSTRACT ii TABLE OF CONTENS iii LIST OF FIGURES v LIST OF TABLES vi CHAPTER 1 INTRODUCTION 1 1.1. Background 1 1.2. Problem Definition 2 1.3. Purpose of the Research 3 1.4. Importance of the Research 3 CHAPTER 2 LITERATURE REVIEW 4 2.1. Dependency Structure in System Reliability 4 2.2. Bayesian Reliability Analysis and Bayesian Aggregation Error 5 2.3. Comparison between Series and Parallel Systems 7 CHAPTER 3 METHODOLOGY 8 3.1. Dependency Modelling with Copula 8 3.2. Bayesian Reliability Model 10 3.2.2. Simple Series Binomial-Beta Systems 10 3.2.3. Simple Parallel Binomial-Beta Systems 11 3.2.4. Aggregate and Disaggregate Analysis 12 3.2.5. Design of Comparison Study 13 3.3. Monte Carlo Simulation and Classification Tree Learning 14 CHAPTER 4 RESULT AND DISCUSSION 19 4.1. Monte Carlo Simulation Study 19 4.2. Copula-Based Reliability Model for Series Systems 19 4.2.1. Aggregate Analysis 20 4.2.2. Disaggregate Analysis 21 4.3. Copula-Based Reliability Model for Parallel Systems 22 4.3.1. Aggregate Analysis 22 4.3.2. Disaggregate Analysis 23 4.4. Preliminary Results 23 4.4.1. Graphical Analysis for Original Parameters 24 4.4.2. Graphical Analysis for Modified Parameters 31 4.5. Classification Tree Results 42 4.5.1. AA−DA Comparison 43 4.5.2. DA−DAI Comparison 50 CHAPTER 5 CONCLUSION 57 5.1. Summary 57 5.2. Practical Recommendations 57 5.3. Limitations 58 REFERENCES 59

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    全文公開日期 2034/02/05 (國家圖書館:臺灣博碩士論文系統)
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