System No. U0002-0506201114420400 使用個別誤判誤差的篩選程序之研究 A study on the screening procedure based on the individual misclassification error 淡江大學 管理科學研究所博士班 Graduate Institute of Management Science 99 2 100 林英博 Ying-Po Lin 895620614 博士 English 2011-06-10 110page advisor - 吳淑妃 co-chair - 歐士田 co-chair - 王智立 co-chair - 張慶輝 co-chair - 吳錦全 co-chair - 林志娟 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 Average outgoing quality Expected cost of quality Individual nonconforming probability Multivariate normal distribution Sequential screening procedure `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。` `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 one-sided sequential screening procedure and a modified two-sided 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.` ```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 one-sided sequential screening procedure based on the individual misclassification error.....5 2.1 The one-sided sequential screening procedure in Tsai and Wu (2002) and Wu and Lu (2001) (Old method).....5 2.2 A modified one-sided 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 one-sided 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 two-sided sequential screening procedure based on the individual misclassification error.....49 4.1 The two-sided sequential screening procedure in Wu and Cheng (2002) (Old method).....49 4.2 A modified two-sided 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 two-sided 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 one-sided 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 one-sided SSP in terms of the AOQ, TIC and EC.....22 Table 2.4.6 Comparison of old method and new method for one-sided DSP in terms of the AOQ, TIC and EC.....23 Table 2.4.7 Comparison of old method and new method for one-sided TSP in terms of the AOQ, TIC and EC.....24 Table 2.4.8 Comparison of old method and new method for one-sided 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 one-sided SSP.....44 Table 3.2.2 The required costs for the modified one-sided DSP.....44 Table 3.2.3 The required costs for the modified one-sided TSP.....45 Table 3.2.4 The required costs for the modified one-sided QSP.....46 Table 4.4.1 Comparison of old method and new method for two-sided SSP in terms of the AOQ, TIC and EC.....64 Table 4.4.2 Comparison of old method and new method for two-sided DSP in terms of the AOQ, TIC and EC.....65 Table 4.4.3 Comparison of old method and new method for two-sided TSP in terms of the AOQ, TIC and EC.....66 Table 4.4.4 Comparison of old method and new method for two-sided QSP in terms of the AOQ, TIC and EC.....68 Table 5.2.1 The required costs for the modified two-sided SSP.....79 Table 5.2.2 The required costs for the modified two-sided DSP.....79 Table 5.2.3 The required costs for the modified two-sided TSP.....80 Table 5.2.4 The required costs for the modified two-sided QSP.....81 List of Figures Figure 2.2.1 IME Z1q for any given eminr and emaxa, q=1,...,r-1 (up), q=r (down) for the modified one-sided SQSP.....12 Figure 3.1.1 Quality cost function cj(y,-Kr), j=1(solid), 2(dotdash), 3(longdash) for the modified one-sided SQSP.....38 Figure 4.2.1 IME Z2q for any given eminr and emaxa, q=1,...,r-1 (up), q=r (down) for the modified two-sided SQSP.....56 Figure 5.1.1 Quality cost function cj(y,Kr1,Kr2), j=1(solid), 2(dotdash), 3(longdash) for the modified two-sided SQSP.....72``` ```Bai, D. 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