有些產品的品質特性並不容易檢查，常因測量費用昂貴、檢驗耗時，或是產品具有破壞性、退化性等問題，因此往往不直接觀察表現變數，而是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，而此方法稱之為篩選程序，但也為了節省檢驗成本和檢驗時間，多站的循序篩選程序方法便因應而生。本研究主要是探討表現變數具有單邊規格及雙邊規格時的循序篩選程序，再以AOQ和TIC為標準來選出最佳的配置組合。
本篇論文提出一修正的循序篩選程序方法，和舊的篩選程序不同的地方在於不需要先決定每個篩選變數之權數，所以將原來加權兩次的程序簡化成只需加權一次，且同樣的對於 個篩選變數放置於 站的所有組合，利用變數變換、矩陣運算及運用多變量常態分配的特性發展出一站、二站和三站的一般性公式，並利用Fortran程式語言算出每一種配置組合的AOQ值和TIC值，以選出最佳的配置組合。此外，三站以上的篩選程序，由於受限於一般性公式積分維度的不易推導，所以改用蒙地卡羅的方法模擬。
最後，我們將利用數個實例，對修正後的循序篩選程序，與先前的方法做比較，結果驗證其表現並沒有比較差，有的甚至更好，所以我們建議使用者，應使用此修正後的循序篩選程序。

The quality characteristics of some products are not easy to check, in order to reduce the cost and time effort of inspection, a modified screening procedure which selects items whose performance variable is within a one-sided specification and two-sided specification based on observing the correlated screening variables according to the individual misclassification error(IME) is proposed. The criterion of average outgoing quality(AOQ) and total inspection cost(TIC) are still used to search for the optimal allocation.
Unlike the original sequential screening procedure, the modified procedure does not need to decide the weights of every screening variable at the beginning stage. Therefore, the modified procedure is only weighting once instead of weighting twice. The generalized formulas for the single stage(SSP), double stage(DSP) and triple stage(TSP) sequential screening procedures are derived by the use of multivariate normal distribution and matrix operation. The Monte Carlo simulation method to simulate the desired probability values for any finite stage of sequential screening procedure, especially for more than three stages due to the complexity of obtaining exact results. 
Several example are used to demonstrate the single stage(SSP), double stage(DSP), triple stage(TSP), quadruple stage(QSP) and the fifth stage(FSP) by the computer program via Fortran IMSL to search for the best allocation. The results show that the modified sequential screening procedure performs similar to the original one and some are even better. Therefore, the modified sequential screening procedure is recommended for practical use.

第一章 緒論	1
1.1 前言	1
1.2 研究背景與動機	1
1.3 本文架構	3
第二章 文獻探討	5
2.1 影響篩選程序的因素	5
2.2 簡單篩選程序之基本模式	8
2.3 特殊篩選程序設計	12
2.4 篩選程序的發展及演進	15
第三章 循序篩選程序的介紹	18
3.1 單邊循序篩選程序	25
3.2 雙邊循序篩選程序	38
第四章 模擬程序	57
第五章 數值實例示範	60
5.1 單邊循序篩選程序實例	60
5.2 雙邊循序篩選程序實例	134
第六章 迴歸分析	182
第七章 結論	185
參考文獻	187 
表目錄
表2-1  篩選程序的發展及演進........................................17
表5-1  四個篩選變數(S.V.)配置於一站篩選程序的可能組合............... 61
表5-2  四個篩選變數(S.V.)配置於二站篩選程序的可能組合............... 61
表5-3  四個篩選變數(S.V.)配置於三站篩選程序的可能組合............... 62
表5-4  四個篩選變數(S.V.)配置於四站篩選程序的可能組合............... 63
表5-5  當四個表現變數配置於單邊一站時，利用公式所得的各個機率值
        (以石油為例)............................................... 64
表5-6  當四個表現變數配置於單邊二站時，利用公式所得的各個機率值
        (以石油為例)............................................... 65
表5-7  當四個表現變數配置於單邊三站時，利用公式所得的各個機率值
        (以石油為例)............................................... 65
表5-8  當四個表現變數配置於單邊四站時，利用模擬所得的各個機率值
        (以石油為例)............................................... 70
表5-9  針對單邊三站，舊法與新法的比較............................. 74
表5-10 針對單邊四站，舊法與新法的比較............................. 78
表5-11 五個篩選變數(S.V.)配置於一站篩選程序的可能組合............... 83
表5-12 五個篩選變數(S.V.)配置於二站篩選程序的可能組合............... 84
表5-13 五個篩選變數(S.V.)配置於三站篩選程序的可能組合............... 85
表5-14 五個篩選變數(S.V.)配置於四站篩選程序的可能組合............... 90
表5-15 五個篩選變數(S.V.)配置於五站篩選程序的可能組合............... 96
表5-16 當五個篩選變數配置於單邊一站時，利用模擬所得的各個機率值
        (以電池為例)............................................... 99
表5-17 當五個篩選變數配置於單邊二站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 100
表5-18 當五個篩選變數配置於單邊三站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 101
表5-19 當五個篩選變數配置於單邊四站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 109
表5-20 當五個篩選變數配置於單邊五站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 121
表5-21 單邊循序篩選程序AOQ及TIC之最佳配置(以電池為例).......... 133
表5-22 當四個篩選變數配置於雙邊一站時，利用公式所得的各個機率值
        (以石油為例).............................................. 134
表5-23 當四個篩選變數配置於雙邊二站時，利用公式所得的各個機率值
        (以石油為例).............................................. 135
表5-24 當四個篩選變數配置於雙邊三站時，利用公式所得的各個機率值
        (以石油為例).............................................. 135
表5-25 當四個篩選變數配置於雙邊四站時，利用模擬所得的各個機率值
        (以石油為例).............................................. 140
表5-26 針對雙邊三站模擬，舊法與新法的比較........................ 142
表5-27 當五個篩選變數配置於雙邊一站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 147
表5-28 當五個篩選變數配置於雙邊二站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 148
表5-29 當五個篩選變數配置於雙邊三站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 149
表5-30 當五個篩選變數配置於雙邊四站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 157
表5-31 當五個篩選變數配置於雙邊五站時，利用模擬所得的各個機率值
        (以電池為例).............................................. 169
表5-32 雙邊循序篩選程序AOQ及TIC之最佳配置(以電池為例)...........181
表8-1  逐步選取法(以石油為例)..................................... 183
表8-2  其他選取法(以石油為例)..................................... 183
表8-3  單邊循序篩選程序AOQ及TIC之最佳配置(以石油為例)...........184
表8-4  雙邊循序篩選程序AOQ及TIC之最佳配置(以石油為例)...........184


 
圖目錄
圖1-1 本文架構圖....................................................4
圖2-1 影響篩選程序的因素............................................5
圖3-1 對任意第 站，若給定 和 時，其 函數之圖形和 , , , 之相對位置............................... 40
圖3-2 針對第 個檢查站(即最後一站)，若給定 時，其 函數之圖形和 , 之相對位置....................................... 41

參考文獻
一、中文部份：
[1]  吳淑妃(民77)，多次篩選的理論與應用，國立中山大學應用數學研究所碩士論文。
[2]  葉惠忠(民79)，二階段單邊篩選之成本模式，國立成功大學工業管理研究所碩士論文。
[3]  蔡憲唐、張保隆、盧昆宏 (民81)，運用多元篩選變數於雙次篩選程序之研究，中國工業工程學刊，第9卷，第1期，45-53。
[4]  蔡憲唐、葉惠忠 (民88)，篩選理論之應用與發展，亞太經濟管理評論，2卷2期，91-107。

二、英文部分：
[1]	Bai, D. S. and Hong, S. H. (1992). Economic screening procedures using a correlated variable with mult-decision alternatives. Naval Research Logistics, 39, pp. 471-485.
[2]	Bai, D. S. and Kim, S. B. (1990). Economic screening procedures in logistic and normal model. Naval Research Logistics, 37, pp. 919-928. 
[3]	Bai, D. S., Kim, S. B. , and Riew, M. C. (1990). Economic screening procedures based on correlated variables. Metrika, 37, pp. 263-280.
[4]	Boddie, J. W. and Owen, D. B. (1976). A screening methods for increasing acceptable product with some parameters unknown. Technometrics, 18, pp. 195-199.
[5]	Boys, R. J. and Dunsmore, I. R. (1986). Screening in a normal model. Journal of the Royal Statistical Society, Series B, 48, pp. 60-69.
[6]	Boys, R. J. and Dunsmore, I. R. (1987). Diagnostic and sampling models in screening. Biometrika, 74, pp. 365-374.
[7]	Butler, D. A. and Lieberman, G. J. (1984). Inspection policies for fault location. Operations Research, 32 , pp. 566-574.
[8]	Drezner, Z. and Wesolowsky, G. O. (1995). Multivariate screening procedure for quality cost minimization. IIE Transactions, 3, pp. 300-304.
[9]	Drury, C. G., Karwan, M. H. ,and Vanderwarker, D. R. (1986). The two inspector problems. IIE Transactions, 18, pp. 174-181.
[10]	Greenshtein, E. and Rabinowitz, G. (1997). Double-stage inspection for screening multi-characteristic items. IIE Transactions, 12, pp. 1057-1061.
[11]	Hong, S. H., Kim, S. B., Kwon, H. M., and Lee, M. K. (1998). Economic design of screening procedure when the rejected items are reprocessed. European Journal of Operational Research, 1, pp. 65-73. 
[12]	Hui, Y. V. (1990). Economic design of complete inspection for bivariate products. International Journal of Production Research, 28, pp. 259-265.
[13]	Johnson, Richard A. and Wichern, Dean W. (2002). Applied Multivariate Statistical Analysis. (5th ed.). The United States of America: Pearson International Edition.
[14]	Lee, M. K. and Jang, J. S. (1997). The optimum target values for a production process with three-class screening. International Journal of Production Economics, 2, 1997, pp. 91-99.
[15]	Li, L. and Owen, D. B. (1979). Two-sided screening procedures in the bivariate case. Technometrics, 21, pp.79-85.
[16]	Lo, Y. and Tang, K. (1990). Economic design of multicharacteristic models for a three class screening procedure. International Journal of Production Research, 28, pp. 2341-2351.
[17]	Longtin, M. D., Wein, L. M., and Welsch, R. E. (1996). Sequential screening in semiconductor manufacturing, I: exploiting spatial dependence. Operations Research, 1. 
[18]	Menzefricke, U. (1984). A decision theoretic approach to some screening problems. Annuls of the Institute of Statistical Mathematics, 36, pp. 485-497.
[19]	Moskowitz, H., Plante, R., and Tsai, H. T. (1991). Single sided economic screening models incorporation individual unit misclassification error and risk preference. European Journal of Operational Research, 53, pp.228-243.
[20]	Moskowitz, H., Plante, R., and Tsai, H. T. (1993). A multistage screening model for evaluation and control of misclassification error in the detection of hypertension. Management Science, 39, pp. 307-321.
[21]	Moskowitz, H. and Tsai, H. T. (1988). A one-sided double screening procedure using individual unit misclassification error. Management Science, 34, pp.1139-1153.
[22]	Ou, J. and Wein, L. M. (1996). Sequential screening in semiconductor manufacturing, II: Exploiting lot-to-lot variability. Operations Research, 1.
[23]	Owen, D. B. (1988). Screening by correlated variables, Encyclopedia of Statistical Sciences 8, edited by Kotz, S. and Johnson, N. L., John Wiley and Sons, New York, NY, pp.309-312.
[24]	Owen, D. B., Li, L. and Chou, Y. M. (1981). Prediction intervals for screening using a measured correlated variate. Technometrics, 23, pp. 165-170.
[25]	Owen, D. B., Mcintire, D. and Seymour, E. (1975). Tables using one or two screening variables to increase acceptance product under one-sided specifications. Journal of Quality Technology, 7, pp.127-138.
[26]	Owen, D. B. and Su, Y. H. (1977). Screening based on normal variables. Technometrics, 19, pp. 65-68.
[27]	Park, J. S., Peters, M. H., and K. Tang. (1991). Optimal inspection policy in sequential screening. Management Science, 37, pp. 1058-1061.
[28]	Raz, T. and Thomas, M. U. (1983). A method for sequencing inspection activities subject to errors. IIE Transactions, 15, pp. 12-18.
[29]	Tang, K. (1988). Design of a two-stage screening procedures using a correlated variable: a loss function approach. Naval Research Logistics, 35, pp.513-533.
[30]	Tang, K. (1990). Design of multi-stage screening procedures for a serial production system. European Journal of Operational Research, 52, pp. 280-290.
[31]	Tang, K. (1987). Economic design of one-sided screening procedure using a correlated Variable. Technometrics, 29, pp. 477-485.
[32]	Tang, K. (1989). Design of product grading procedure. Decision Sciences, 21, pp.434-445.
[33]	Tang, K. and Schneider, H. (1987). The economic effects of inspection error on a complete inspection plan. IIE Transactions, 19, pp.421-428.
[34]	Tang, J. and Tang, K. (1989a). A two-sided screening procedure using several correlated Variables, IIE Transactions, 21, pp. 333-336.
[35]	Tang, J. and Tang, K. (1989b). Design of product specifications for multi-characteristic inspection. Management Science, 35, pp. 743-756.
[36]	Tang, J. and Tang, K. (1994). Design of screening procedures: a review. Journal of Quality Technology, 3, pp.209-226.
[37]	Taylor, H. C. and Russell, J. T. (1939). The relationship of validity coefficients to the practical effectiveness of test in selection: Discussion and Tables. Journal of Psychology, 23 , pp. 565-578.
[38]	Thomas, J. G., Owen, D. B., and Gunst, R. F. (1977). Improving the use of educational tests as evaluation tools. Journal of Educational Statistics, 2, pp. 55-77.
[39]	Tsai, H. T. (1986). Single and double screening procedures using Individual misclassification error. Ph.D. Thesis, Purdue University. 
[40]	Tsai, H. T., Moskowitz, H., and Tang, J. (1995). A One-sided single screening procedure based on individual unit misclassification error. IIE Transactions, 27, pp. 695-706.
[41]	Wu, S. F. and Cheng, M. Y. (2002). A two-sided sequential screening procedure based on individual misclassification error. Computational Statistics and Data Analysis, 40, pp. 375-391.
[42]	Wu, S. F. and Lu, D. L. (2001). Sequential Screening Procedure by Simulation Methodology, International Journal of Information and Management Sciences, 12, 4, pp.41-53.