
系統識別號 
U00020506201114420400 
中文論文名稱

使用個別誤判誤差的篩選程序之研究 
英文論文名稱

A study on the screening procedure based on the individual misclassification error 
校院名稱 
淡江大學 
系所名稱(中) 
管理科學研究所博士班 
系所名稱(英) 
Graduate Institute of Management Science 
學年度 
99 
學期 
2 
出版年 
100 
研究生中文姓名 
林英博 
研究生英文姓名 
YingPo Lin 
學號 
895620614 
學位類別 
博士 
語文別 
英文 
口試日期 
20110610 
論文頁數 
110頁 
口試委員 
指導教授吳淑妃 委員歐士田 委員王智立 委員張慶輝 委員吳錦全 委員林志娟

中文關鍵字 
平均出廠品質
期望品質成本
個別誤判誤差機率
多變量常態分配
循序篩選程序

英文關鍵字 
Average outgoing quality
Expected cost of quality
Individual nonconforming probability
Multivariate normal distribution
Sequential screening procedure

學科別分類 

中文摘要 
因為有些產品的品質特性檢查困難、昂貴或是具有退化性，因此藉由觀察數個和表現變數有關的篩選變數，由它們來判定產品是否被接受。此方法稱之為篩選程序。為了節省檢驗成本和檢驗時間，因此進一步發展出循序篩選程序。本論文主題主要是針對使用個別誤判誤差的循序篩選程序之研究。本研究提出一修正單邊循序篩選程序和一修正雙邊循序篩選程序來簡化舊的循序篩選程序。我們以原油提煉汽油的例子來做新法和舊法的數值比較，結果顯示新法的期望成本非常接近舊法或比舊法好。所以我們推薦使用新法，因它有不用加權兩次較為簡化的優點，且其成本表現也比舊法好。對修正的循序篩選程序，我們考慮三種品質成本函數的期望總成本，其中期望總成本是總檢查成本、期望拒絕成本和期望品質成本的總和。當數個篩選變數配置在多站時，我們可推導出所有所需要的機率和三種總期望成本的一般化公式。因此，即使是三站以上的篩選程序，所需要的機率和成本都可以推導求得。並以最小期望總成本為準則來找出最適配置。最後，我們給兩個例子來示範本研究所提出之修正循序篩選程序在三種總期望成本下之最適配置的選擇。 
英文摘要 
Since the measuring on the quality characteristics of some products may be hard, expensive or degenerative, the item is determined to be accepted or not based on the observed screening variables which are correlated with the performance variable. The screening procedure is thus arisen. In order to reduce the cost and time effort of inspection, a sequential screening procedure is developed. This dissertation is focusing on the study of the sequential screening procedure based on the individual misclassification error. We propose a modified onesided sequential screening procedure and a modified twosided sequential screening procedure to simplify the existing procedures. We use the example of refining gasoline from the available crude oil to do the numerical comparison of the new method and the old method, and the results show that the modified sequential screening procedure performs very close to or better than the old one. Since the new method has the advantage of simplifying the old method by only weighting the screening variables once instead of weighting twice and has better performance than the old method, the new method is recommended for use. For the modified screening procedures, we also consider the expected total costs of three kinds of quality cost functions based on the individual misclassification error, where the expected total cost is the sum of the total inspection cost, the expected cost of rejection and the expected cost of quality. We derive the generalized computational formulas for the desired probability quantities and three kinds of expected total costs when k screening variables are allocated into r stages, where r and k are positive integers, k≦r and r can be more than 3. The criterion of minimum expected total cost is used to search for the optimal allocation. At last, we give two examples to illustrate the selection of the optimal allocation combination for the sequential screening procedure under three kinds of expected total costs. 
論文目次 
Contents
Acknowledgments in Chinese.....I
Abstract in Chinese.....II
Abstract in English.....III
Contents.....IV
List of Tables.....VI
List of Figures.....VIII
Chapter 1 Introduction.....1
1.1 Literature review.....1
1.2 Organization of this dissertation.....3
Chapter 2 A modified onesided sequential screening procedure based on the individual misclassification error.....5
2.1 The onesided sequential screening procedure in Tsai and Wu (2002) and Wu and Lu (2001) (Old method).....5
2.2 A modified onesided sequential screening procedure (New method).....10
2.3 All required characteristic quantities and expected costs for the new method.....15
2.4 The numerical comparison of new method and old method.....19
2.5 Numerical example.....27
Chapter 3 The optimal allocation combination for the modified onesided sequential screening procedure based on the individual misclassification error.....37
3.1 Expected total costs.....37
3.2 Numerical examples.....42
Chapter 4 A modified twosided sequential screening procedure based on the individual misclassification error.....49
4.1 The twosided sequential screening procedure in Wu and Cheng (2002) (Old method).....49
4.2 A modified twosided sequential screening procedure (New method).....54
4.3 All required characteristic quantities and expected costs for the new method.....58
4.4 The numerical comparison of new method and old method.....62
4.5 Numerical example.....69
Chapter 5 The optimal allocation combination for the modified twosided sequential screening procedure based on the individual misclassification error.....71
5.1 Expected total costs.....71
5.2 Numerical examples.....77
Chapter 6 Conclusions.....84
References.....86
Appendix A: Proof of Theorem 2.2.1.....88
Appendix B: Proof of Theorem 2.2.2.....91
Appendix C: Proof of three kinds of quality cost functions for the modified onesided sequential screening procedure.....97
Appendix D: Proof of Lemma 4.3.1.....103
Appendix E: Proof of Theorem 5.1.1.....107
List of Tables
Table 2.4.1 1 allocation combination for SSP with four screening variables.....21
Table 2.4.2 14 allocation combinations for DSP with four screening variables.....21
Table 2.4.3 36 allocation combinations for TSP with four screening variables.....21
Table 2.4.4 24 allocation combinations for QSP with four screening variables.....21
Table 2.4.5 Comparison of old method and new method for onesided SSP in terms of the AOQ, TIC and EC.....22
Table 2.4.6 Comparison of old method and new method for onesided DSP in terms of the AOQ, TIC and EC.....23
Table 2.4.7 Comparison of old method and new method for onesided TSP in terms of the AOQ, TIC and EC.....24
Table 2.4.8 Comparison of old method and new method for onesided QSP in terms of the AOQ, TIC and EC.....26
Table 2.5.1 1 allocation combination for SSP with five screening variables.....29
Table 2.5.2 30 allocation combinations for DSP with five screening variables.....29
Table 2.5.3 150 allocation combinations for TSP with five screening variables.....29
Table 2.5.4 240 allocation combinations for QSP with five screening variables.....31
Table 2.5.5 120 allocation combinations for FSP with five screening variables.....35
Table 3.2.1 The required costs for the modified onesided SSP.....44
Table 3.2.2 The required costs for the modified onesided DSP.....44
Table 3.2.3 The required costs for the modified onesided TSP.....45
Table 3.2.4 The required costs for the modified onesided QSP.....46
Table 4.4.1 Comparison of old method and new method for twosided SSP in terms of the AOQ, TIC and EC.....64
Table 4.4.2 Comparison of old method and new method for twosided DSP in terms of the AOQ, TIC and EC.....65
Table 4.4.3 Comparison of old method and new method for twosided TSP in terms of the AOQ, TIC and EC.....66
Table 4.4.4 Comparison of old method and new method for twosided QSP in terms of the AOQ, TIC and EC.....68
Table 5.2.1 The required costs for the modified twosided SSP.....79
Table 5.2.2 The required costs for the modified twosided DSP.....79
Table 5.2.3 The required costs for the modified twosided TSP.....80
Table 5.2.4 The required costs for the modified twosided QSP.....81
List of Figures
Figure 2.2.1 IME Z1q for any given eminr and emaxa, q=1,...,r1 (up), q=r (down) for the modified onesided SQSP.....12
Figure 3.1.1 Quality cost function cj(y,Kr), j=1(solid), 2(dotdash), 3(longdash) for the modified onesided SQSP.....38
Figure 4.2.1 IME Z2q for any given eminr and emaxa, q=1,...,r1 (up), q=r (down) for the modified twosided SQSP.....56
Figure 5.1.1 Quality cost function cj(y,Kr1,Kr2), j=1(solid), 2(dotdash), 3(longdash) for the modified twosided SQSP.....72 
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