
系統識別號 
U00022905201212433000 
中文論文名稱

使用代理變數進行統計製程管制 
英文論文名稱

Implementing Statistical Process Control Using Surrogate
Variables 
校院名稱 
淡江大學 
系所名稱(中) 
管理科學學系博士班 
系所名稱(英) 
Doctoral Program, Department of Management Sciences 
學年度 
100 
學期 
2 
出版年 
101 
研究生中文姓名 
江俊佑 
研究生英文姓名 
JyunYou Chiang 
學號 
895620622 
學位類別 
博士 
語文別 
英文 
口試日期 
20120518 
論文頁數 
71頁 
口試委員 
指導教授蔡宗儒 委員歐陽良裕 委員劉玉龍 委員林宗儀 委員邵曰仁 委員侯家鼎 委員李燊銘 委員吳碩傑

中文關鍵字 
兩階段的經濟管制圖
最適的篩選過程
代理變數

英文關鍵字 
Noncentral chisquare chart
Profit function
Screening limits
Surrogate variable
Twostage control charts

學科別分類 

中文摘要 
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。 
英文摘要 
In this dissertation, two approaches are proposed for statistical quality control applications based on surrogate variables. A twostage 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 outofcontrol 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. 
論文目次 
Contents
1 Introduction 1
1.1 Problem Statement 1
1.2 Literature Review and Motivation 2
2 The Economic TwoStage Design of Noncentral Chisquare Chart 8
2.1 The Noncentral Chisquare Charts 9
2.2 The TwoStage Noncentral Chisquare 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 TwoStage 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 twostage 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 
參考文獻 
[1] O. Carlsson (1984). Determining the most profitable process level for a production process under different sales conditions. Journal of Quality Technology, 16,
pp. 4449.
[2] K. Tang, J. Lo (1993). Determination of the optimal process mean when inspection is based on a correlated variable. IIE Transactions, 25, pp. 6672.
[3] D.S. Bai, M.K. Lee (1993). Optimal target values for a filling process when inspection is based on a correlated variable. International Journal of Production Economics, 32, pp. 327334.
[4] D.S. Bai, H.M. Kwon, M.K. Lee (1995). An economic twostage screening procedure with a prescribed outgoing quality in logistic and normal models. Naval Research Logistics, 42, pp. 10811097.
[5] M.K. Lee, S.H. Hong, E.A. Elsayed (2001). The optimum target value under single and twostage screenings. Journal of Quality Technology, 33, pp. 506514.
[6] M.K. Lee, E.A. Elsayed (2002). Process mean and screening limits for filling processes under twostage screening procedure. European Journal of Operational Research, 138, pp. 118126.
[7] A.F.B. Costa, M.S. De Magalhaes (2005). Economic design of twostage Xbar chart: The Markov chain approach. International Journal of Production Economics, 95, pp. 920.
[8] S.O. Samuelsen, H. Anestad, A. Skrondal (2007). Stratified casecohort analysis of general cohort sampling designs, Scandinavian Journal of Statistics, 34, pp. 103119.
[9] J.T. Leek, J.D. Storey (2008). A general framework for multiple testing dependence, Proceedings of the National Academy of Sciences of the United States of America, 105, pp. 1871818723.
[10] S.H. Hong (2009). Development of the optimal screening procedures for normal and logistic models, International Journal of Quality Engineering and Technology, 1, pp. 6274.
[11] Y. Nakagawa, S. Miyazaki (1981). Surrogate constraints algorithm for reliability optimization problems with two constraints, IEEE Transactions on Reliability, R30, pp. 175180.
[12] Q. Wang, R. Zhang (2009). Statistical estimation in varying coefficient models with surrogate data and validation sampling, Journal of Multivariate Analysis, 100, pp. 23892405.
[13] D. Manner, J.J.W. Seaman, D.M. Young (2004). Bayesian methods for regression using surrogate variables. Biometrical Journal, 46, pp. 750759.
[14] J. Lee, W.J. Kwon (1999). Economic design of a twostage control chart based on both performance and surrogate variable. Naval Research Logistics, 46, pp. 958977.
[15] A.F.B. Costa, M.A. Rahim (2000). Joint Xbar and R charts with two stage samplings. Quality and Reliability Engineering International, 20, pp. 699708.
[16] M.A. Rahim, A.F.B. Costa (2000). Joint economic design of Xbar and R charts under Weibull shock models. International Journal of Production Research, 38, pp. 28712889.
[17] F.F. Gan (1995). Joint monitoring of process mean and variance using exponentially weighted moving average control charts. Technometrics, 37, pp. 446453.
[18] S.L. Albin, L. Kang, and G. Sheha (1997). An X and EWMA chart for individual observations. Journal of Quality Technology, 29, pp. 4148.
[19] G. Chen, S.W. Cheng, H. Xie (2001). Monitoring process mean and variability with one EWMA chart. Journal of Quality Technology, 33, pp. 223233.
[20] A.F.B. Costa (1998). Joint Xbar and R charts with variable parameters. IIE Transactions, 30, pp. 505514.
[21] A.F.B. Costa (1999). Joint Xbar and R charts with variable sample sizes and sampling intervals. Journal of Quality Technology, 31, pp. 387397.
[22] M.S. De Magalhaes, F.D. Moura Neto (2005). Joint economic model for totally adaptive Xbar and R charts. European Journal of Operational Research, 161, pp.
148161.
[23] M.R. Reynolds, Z.G. Stoumbos (2001). Monitoring the process mean and variance using individual observations and variable sampling intervals. Journal of Quality Technology, 33, pp. 181205.
[24] A.F.B. Costa, M.A. Rahim (2004). Monitoring process mean and variability with one noncentral Chisquare chart. Journal of Applied Statistics, 31, pp. 11711183.
[25] A.F.B. Costa, M.S. De Magalhaes (2007). An adaptive chart for monitoring the process mean and variance. Quality and Reliability Engineering International, 23, pp. 821831.
[26] C.H. Springer (1951). A method of determining the most economic position of a process mean. Industrial Quality Control, 8, pp. 3639.
[27] D.C. Bettes (1962). Finding an optimum target value in relation to a fixed lower limit and an arbitrary upper limit. Applied Statistics, 11, pp. 202210.
[28] D.Y. Golhar (1987). Determination of the best mean contents for a canning problem. Journal of Quality Technology, 19, pp. 8284.
[29] D.Y. Golhar, S.M. Pollock (1988). Determination of the optimal process mean and upper limit for a canning problem. Journal of Quality Technology, 20, pp. 188192.
[30] W.G. Hunter, C.D. Kartha (1977). Determining the most profitable target value for a production process. Journal of Quality Technology, 9, pp. 176181.
[31] S. Bisgaard, W.G. Hunter, L. Pallesen (1984). Economic selection of quality of manufactured product. Technometrics, 26, pp. 918.
[32] K. Tang (1988). Design of a twostage screening procedure using correlated variables: A loss function approach. Naval Research Logistics, 35, pp. 513533.
[33] C.T. Kim, K. Tang, M. Peters (1994). Design of a twostage procedure for threeclass screening. European Journal of Operational Research, 79, pp. 431442.
[34] M.K. Lee, J.S. Jang (1997). The optimum target values for a production process with threeclass screening. International Journal of Production Economics, 49, pp. 9199.
[35] S.H. Hong, K.B. Kim, H.M. Kwon, M.K. Lee (1998). Economic design of screening procedures when the rejected items are reprocessed. European Journal of Operational Research, 108, pp. 6573.
[36] C.H. Chen, H.S. Kao (2009). The determination of optimum process mean and screening limits based on quality loss function. Expert Systems with Applications, 36, pp. 73327335.
[37] M.K. Lee, S.H. Hong, H.M. Kwon, S.B. Kim (2000). Optimum process mean and screening limits for a production process with threeclass screening. International Journal of Reliability, Quality and Safety Engineering, 7, pp. 179190.
[38] W.A. Fuller (1987). Measurement error models. Wiley: New York, pp. 15.
[39] S.M. Ross (1992). Applied Probability Models with Optimization Applications. Dover, New York, pp. 119168.
[40] G. N. Vanderplaats and H. Sugimoto (1986). A generalpurpose optimization program for engineering design. Computers & Structures, 24, pp. 1321.
[41] M.K. Lee, G.S. Kim (1994). Determination of the optimal target values for a filling process when inspection is based on a correlated variable. International Journal of Production Economics, 37, pp. 205213.
[42] M.R. Panagos, R.G. Heikes, D.C. Montgomery (1985). Economic design of Xbar control charts for two manufacturing process models. Naval Research Logistics,
32, pp. 631464.

論文使用權限 
同意紙本無償授權給館內讀者為學術之目的重製使用，於20120606公開。同意授權瀏覽/列印電子全文服務，於20120606起公開。 


