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研究生: 劉亦婷
Yi-Ting LIU
論文名稱: 相依組件並聯系統的貝氏可靠度分析
Bayesian Reliability Analysis of Parallel Systems with Dependent Components
指導教授: 林希偉
Shi-Woei Lin
口試委員: 曹譽鐘
Yu-Chung Tsao
黃麗妃
Li-Fei Huang
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: 2016
畢業學年度: 104
語文別: 英文
論文頁數: 112
中文關鍵詞: Copula貝氏可靠度整合式分析非整合式分析相依組件蒙地卡羅模擬決策樹
外文關鍵詞: Copula, Bayesian reliability, aggregate analysis, disaggregate analysis, dependent components, Monte Carlo simulation, classification tree
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  • 相依組件系統之貝氏可靠度分析方法主要有整合式分析、非整合式分析及簡化式非整合式分析三種。其中,整合式分析先產生系統先驗分配再透過系統故障資訊更新分配,具有低成本及實用的優點。非整合式分析使用較高成本的組件資訊來更新組件之先驗分配,再產生系統故障機率分配,花費的成本與分析複雜度都大幅提高,但卻可提供準確的結果。在實務上的另一考量則是簡化的非整合式分析,此方法忽視組件相依的情況,使用組件獨立的假設來分析系統可靠度。本研究的目的在於找出在貝氏可靠度分析中影響不同分析方法的相對誤差的關鍵因子與參數,透過Copula方法描述組件之間的相依性,並使用蒙地卡羅模擬系統失效事件的資料,最後使用分類樹來分類並預測不同情況(即不同參數組合下)最合適的分析方法以提供管理者一個可靠的決策法則。


    In Bayesian reliability analysis, three approaches can be used to evaluate the reliability of a system. An aggregate analysis propagates component prior distributions first and then preforms Bayesian updates of aggregated prior distribution with system-level data, a disaggregate analysis performs Bayesian updates with component-level data first and then propagates component posterior distribution through the risk model, and the simplified disaggregate analysis also performs Bayesian updates with component-level data but assumes that the failure of the components are independent. Although the aggregate analysis and simplified disaggregate analysis are more practical and less expensive, the disaggregate analysis provides more accurate results. This work aims to identify the key factors that affect the magnitude of relative errors of three different approaches. In particular, a copula-based Bayesian reliability models for parallel system with dependent components (including failure rate and failure probability cases) were investigated by employing Monte Carlo simulation. Classification tree models were also used to provide a reliable guideline on selecting an appropriate analysis approach under different circumstances.

    摘要 i Abstract ii 致謝 iii Table of Content iv List of Figure vi List of Table ix CHAPTER 1. Introduction 1 CHAPTER 2. Literature Review 4 2.1. Bayesian Reliability Analysis 4 2.2. Bayesian Aggregation Error 5 2.3. Dealing with Dependency Issue 7 CHAPTER 3. Methodology 10 3.1. Modeling for Copula-Based Bayesian Reliability 10 3.1.1. Simple Parallel System for Probability Case 10 3.1.2. Disaggregate and Aggregate Analyses for Probability Case 11 3.1.3. Simple Parallel System for Product of a probability and a Frequency 14 3.1.4. Disaggregate and Aggregate Analyses for Failure Rate Cases 15 3.1.5. Bivariate Copula 17 3.2. Simulating Pseudo data by using Monte Carlo simulation method 19 3.3. Regionalized Sensitivity Analysis 20 3.4. Classification Modeling 23 CHAPTER 4. Copula-Based Bayesian Reliability for Failure Probability Case 28 4.1. Copula-Based Bayesian Reliability Model 28 4.1.1. Disaggregate Analysis 29 4.1.2. Aggregate Analysis 30 4.1.3. Simplified Disaggregate Analysis 30 4.1.4. General results 32 4.2. Monte Carlo Simulation Study and Regionalized Sensitivity Analysis 35 4.2.1. Separated Scheme Analysis 38 4.2.2. Integrated Scheme Analysis 41 4.3. Classification Tree 45 4.3.1. Incorporating Modified parameters as the Input Factors 50 4.3.2. Classification Tree by Considering Modified Parameters as Input Factors 56 4.4. Results of Classification Tree by Considering Modified Parameters as Input Factors 58 CHAPTER 5. Copula-Based Bayesian Reliability for Failure Rate Case 62 5.1. Copula-Based Bayesian Reliability Model 62 5.1.1. Disaggregate Analysis 63 5.1.2. Aggregate Analysis 64 5.1.3. Simplified Disaggregate Analysis 64 5.1.4. General results 66 5.2. Monte Carlo Simulation Study and Regionalized Sensitivity Analysis 69 5.2.1. Separated Scheme Analysis 70 5.2.2. Integrated Scheme Analysis 73 5.3. Classification Tree 76 5.3.1. Imbalanced data set 76 5.3.2. Incorporating Modified parameters as the Input Factors 79 5.4. Results of Classification Tree by Considering Modified Parameters as the Input Factors 85 CHAPTER 6. Conclusion 89 Reference 93 Appendix 97

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