假設一個生產過程中，通過篩選的產品可能被出售到主要市場或次要市場，被拒絕的產品則需要重工。在此假設下，本論文提出一個利潤模型來決定最佳的生產製程平均水準及篩選界限。當替代變數被使用來取代績效變數而導致產品在篩選時被錯誤分類的情況發生時，本文提出的方法考慮合理的懲罰成本及使用一個適合的機率模型來建立期望利潤模型以改進Lee et al. [12] 所提出的方法。本文詳細介紹尋求最佳製程平均及篩選界限的方法，並舉一例子做說明。


                             表單編號：ATRX-Q03-001-FM030-01

The thesis provides a new profit model to determine the optimum process mean level and screening limits for a production process, where the accepted item is sold on one of two alternate markets, and the rejected item is reworked.
The proposed method uses a cost function with reasonable penalty incurred by misclassification for a product with the surrogate variable. Moreover, a suitable probability distribution is suggested to improve the performance
of the method proposed by Lee et al. [12]. Methods of finding the optimum process mean level and the screening limits are given and an illustrative example is presented.


                             表單編號：ATRX-Q03-001-FM031-01

Contents
1 Introduction                                           1
2 Literature Review                                      4
3 The Proposed Method                                    8
3.1 Optimum Screening Procedure for a Modified Profit  Model                                                    8
3.2 Generalized Profit Models  . . . . . . . . . . . . . 13
4 Example and Sensitivity Study                          15
4.1 Example . . . . .        . . . . . . . . . . . . . . 15
4.2 Sensitivity Study . . . . . . . . . .    . . . . . . 17
5 Conclusions                                            29

List of Tables
4.1 Interval probabilities for Models I, II and III(d1 = 6.5)                                                      20
4.2 Effect of chi              . . . . . . .. . . . . . . 21
4.3 Effect of sigma . . . . . . . . . .       . . . . . . 21
4.4 Effect of rho  . . . .    . . . . . . . . . . . . . . 22
4.5 Effect of b. . . . . . . . . . . . . . .  . . . . . . . . . . . . . 22
4.6 Effect of cx. . . . .     . . . . . . . . . . . . . . 23

List of Figures
4.1 Effect of chi  on profit models (a) PI (b) PII (c) PIII  24
4.2 Effect of sigmay on profit models (a) PI (b) PII (c) PIII 25
4.3 Effect of rho on the profit model (a) PII (b) PIII . 26
4.4 Effect of b on the profit model (a) PII (b) PIII . . 27
4.5 Effect of cx on the profit model (a) PII (b) PIII . . 28

Bibliography
[1] Bai, D.S., Kwon, H.M., Lee, M.K. (1995). An economic two-stage screening procedure with a prescribed outgoing quality in logistic and normal models. Naval Research
Logistics, 42: 1081-1097.
[2] Bai, D.S., Lee, M.K. (1993). Optimal target values for a filling process when inspection is based on a correlated variable. International Journal of Production Economics,
32: 327-334.
[3] Bettes, D.C. (1962). Finding an optimum target value in relation to a fixed lower limit and an arbitrary upper limit. Applied Statistics, 11: 202-210.
[4] Bisgaard, S., Hunter, W.G., Pallesen, L. (1984). Economic selection of quality of manufactured product. Technometrics, 26: 9-18.
[5] Carlsson, O. (1984). Determining the most profitable process level for a production process under different sales conditions. Journal of Quality Technology, 16: 44-49.
[6] Chen, C.H. and Kao, H.S. (2008). The determination of optimum process mean and screening limits based on quality loss function. Expert Systems with Applications.
[7] Golhar, D.Y. (1987). Determination of the best mean contents for a canning problem. Journal of Quality Technology, 19: 82-84.
[8] Golhar, D.Y., Pollock, S.M. (1988). Determination of the optimal process mean and upper limit for a canning problem. Journal of Quality Technology, 20: 188-192.
[9] Hong, S.H., Kim, K.B., Kwon, H.M. and Lee, M.K. (1998). Economic design of screening procedures when the rejected items are reprocessed. European Journal of Operational Research, 108: 65-73.
[10] Hunter, W.G., Kartha, C.D. (1977). Determining the most profitable target value for a production process. Journal of Quality Technology, 9: 176-181.
[11] Kim, C.T., Tang, K. and Peters, M. (1994). Design of a two-stage procedure for three-class screening. European Journal of Operational Research, 79: 431-442.
[12] Lee, M.K., Hong, S.H., Kwon, H.M., Kim, S.B. (2000). Optimum process mean and screening limits for a production process with three-class screening. International Journal of Reliability, Quality and Safety Engineering, 3: 179-190.
[13] 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, 49: 91-99.
[14] Lee, M.K., Hong S.H. and Elsayed, E.A. (2001). The optimum target value under single and two-stage screenings. Journal of Quality Technology, 33: 506-514.
[15] Lee, M.K. and Elsayed, E.A. (2002). Process mean and screening limits for filling processes under two-stage screening procedure. European Journal of Operational Research, 138: 118-126.
[16] Springer, C.H. (1951). A method of determining the most economic position of a process mean. Industrial Quality Control, 8: 36-39.
[17] Tang, K. (1988). Design of a two-stage screening procedure using correlated variables: A loss function approach. Naval Research Logistics, 35: 513-533.
[18] Tang, K., Lo, J. (1993). Determination of the optimal process mean when inspection is based on a correlated variable. IIE Transactions, 25: 66-72.