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。

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.

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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