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系統識別號 U0002-2905201212433000
中文論文名稱 使用代理變數進行統計製程管制
英文論文名稱 Implementing Statistical Process Control Using Surrogate Variables
校院名稱 淡江大學
系所名稱(中) 管理科學學系博士班
系所名稱(英) Doctoral Program, Department of Management Sciences
學年度 100
學期 2
出版年 101
研究生中文姓名 江俊佑
研究生英文姓名 Jyun-You Chiang
學號 895620622
學位類別 博士
語文別 英文
口試日期 2012-05-18
論文頁數 71頁
口試委員 指導教授-蔡宗儒
委員-歐陽良裕
委員-劉玉龍
委員-林宗儀
委員-邵曰仁
委員-侯家鼎
委員-李燊銘
委員-吳碩傑
中文關鍵字 兩階段的經濟管制圖  最適的篩選過程  代理變數 
英文關鍵字 Non-central chi-square chart  Profit function  Screening limits  Surrogate variable  Two-stage control charts 
學科別分類
中文摘要 本論文使用代理變數針對統計製程管制提出兩種新的統計方 法,在第一個方法中,我們建立一個兩階段的經濟管制圖,藉由輪 流監控績效變數及它的代理變數以利對由績效變數之製程平均數偏 移或者製程變異數偏移所引起的製程失控快速預警。在第二個方法 中,我們利用一個廣義的利潤函數及代理變數,針對績效變數發展 出一個最適的篩選過程,以設定績效變數之最佳製程平均水準及篩 選界限。除使用數值方法來評估兩種新統計方法的績效外,本論文 並使用實例說明如何使用建議的統計方法。研究中發現基於經濟的 考量,這兩種新方法皆能顯著的改進現有方法的成效。
英文摘要 In this dissertation, two approaches are proposed for statistical quality control applications based on surrogate variables. A two-stage economic control chart is developed in first approach to monitor either the performance variable or its surrogate variable in an alternating fashion to quickly alarm for out-of-control signals caused by the mean shift or the variance shift of the performance variable. In second approach, an optimum screening procedure is developed based on a new generalized profit function using the surrogate variable of the performance variable to set up the optimal process mean level of the performance variable and the screening limits. Numerical studies are conducted to evaluate the performance of the proposed methods. Examples are presented to demonstrate the applications of two proposed methods. Both proposed approaches result in a significant improvement over the existing methods in term of the economic viewpoint.
論文目次 Contents
1 Introduction 1
1.1 Problem Statement 1
1.2 Literature Review and Motivation 2
2 The Economic Two-Stage Design of Non-central Chi-square Chart 8
2.1 The Non-central Chi-square Charts 9
2.2 The Two-Stage Non-central Chi-square Charts 10
2.3 The Cost Model 16
3 An Optimum Screening Procedure Using Surrogate Variables 19
3.1 Traditional Optimum Screening Procedures 20
3.2 The Optimum Screening Procedure for a Modified Profit Model 24
3.3 A General Case of the Profit Function 27
4 Examples 30
4.1 Example 1 30
4.2 Example 2 34
5 Numerical Results 37
5.1 Numerical Results for the Economic Two-Stage NCS Charts 37
5.2 Comparison of the Expected Profit Based on Various Optimum Screening Procedures 50
6 Conclusions 59
Appendices 62
Bibliography 66
List of Figures
2.1 The flowchart of the proposed two-stage charting design 13
5.1 Effect of X on w1 and w2 for E(PIII) 54
5.2 Effect of sigmax0 on w1 and w2 for E(PIII) 54
5.3 Effect of b on w1 and w2 for E(PIII) 55
5.4 Effect of cy on w1 and w2 for E(PIII) 55
5.5 Effect of X on the proportions of different markets for E(PIII) 56
5.6 Effects of sigmax0 on the proportions of different markets for E(PIII) 56
5.7 Effects of rho on the proportions of different markets for E(PIII) 57
5.8 Effects of cy on the proportions of different markets for E(PIII) 57
5.9 Compares the expected profits between E(PG) and other designs 58
List of Tables
4.1 Control charts and their expected net incomes per unit time 33
4.2 The expected net income per unit time for various rho 34
4.3 The optimum process mean level, screening limits of surrogate variable and expected profit for various profit functions 36
5.1 Cost and process parameters for test examples 39
5.2 The optimum design for test examples 39
5.3 The optimum designs when using cost components in Table 5.1 51
5.4 The values of mux0III*, E(PII) and E(PIII) for various X, sigmax0, rho, b and cx 52
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