先前有關指數加權移動平均(EWMA)管制圖之研究大部份都針對製程平均值偏移進行監控。事實上，當製程變異值增加時，對於產品品質的影響，也許更加的重要。
由於產品品質產生變異的原因包括製程平均值與變異數的改變，所以，本論文主要在運用廣泛加權移動平均管制圖同時監控製程偏移與變異。根據廣泛加權移動平均(GWMA)管制圖之通用模式可推導出個別值修華特(Shewhart X)及指數加權移動平均管制圖均為其特例，也就是廣泛加權移動平均通用模式提供上述特殊參數組合下之特例管制圖一個共同的理論基礎，進而在應用上能充份運用此兩特例管制圖之參數特性，強化廣泛加權移動平均管制圖之整體偵測敏感性。
本論文利用數值模擬分析方式，驗証廣泛加權移動平均管制圖對於製程發生偏移與變異偵測性之有利參數設計。最後，經由所掌握之管制圖參數特性，組合一系列的X-GWMA管制圖進行模擬評估，並得到平均連串長度具良好特性之研究結果外，因可分別將兩種統計量及管制界限繪製於同一張管制圖內，而產生一張合併的管制圖。藉由電腦分別產生兩種管制界限及統計量之顏色差異，對於管制圖之分析，將更具解讀性。
因此，本論文所推廣之個別觀測值管制圖通用模式與參數設計之模擬研究成果，對於自動化產業在監控製程方面，除了具有推廣之彈性與導入之簡易性外，對於製程監控管理人員而言，將更具實務性之吸引力。

Most applications of the EWMA control chart for monitoring processes depend on detecting shifts in the process mean. The problem of detecting an increase in process variability, which can also strongly affect the quality of products is perhaps more important.
This study develops the simultaneous monitoring of process mean and process variability using a single control chart based on a generalization of the exponentially weighted moving average (EWMA) control chart. This generalized chart, is called herein the generally weighted moving average (GWMA) control chart. The GWMA provides a unified treatment of the special cases: the Shewhart X chart and the EWMA chart. Additionally, the GWMA scheme includes characteristics of one or more of the special cases.
The performance of simultaneous monitoring reveals that the GWMA exhibits favorable average run length (ARL) properties and so quickly detects increases in both the mean and variability of the process.A simulation is performed to evaluate the ARL to false alarm and to monitor the change in the process of the X chart, the GWMA chart, and a group of composite X-GWMA control charts. This study recommend the use of the X and GWMA chart, which is practical in that both charts are plotted on one, easily interpreted graph. Additionally, an extensive comparison shows that the X-GWMA control chart is more sensitive than the other control charts in monitoring the small changes in the process mean and variability.
Furthermore, the developed general model is more flexible and easily implemented and so is attractive and useful to practitioners. The results of this study can be applied to monitor the process mean and variability in automated industries.

Albin S. L., Kang L., Shea G., (1997). An X and EWMA chart for individual observations. Journal of Quality Technology, 29, 41-48.
Amin, R. W., Wolff, H., Besenfelder W., Baxley R. JR., (1999). EWMA control charts for the smallest and largest observations. Journal of Quality Technology, 31(2), 189-206.
Borror, C. M., Montgoery, D. C., and Runger, G. C., (1999). Robustness of the EWMA control chart to non-normality, Journal of Quality Technology, 31, 309-316.
Chang, T. C., and Gan, F. F., (2004). Shewhart charts for monitoring the variance components. Journal of Quality Technology, 36, 293-308.
Chen, G., Cheng S. W., and Xie, H., (2001). Monitoring process mean and variability with one EWMA chart. Journal of Quality Technology, 33(2), 223-233.
Chen, G., Cheng S. W., and Xie, H., (2004). A new EWMA control chart for monitoring both location and dispersion. Quality Technology & Quantitative Management, 1(2),217-231.
Crowder, S.V., (1987a). Computation of ARL for combined individual measurement and moving range charts. Journal of Quality Technology, 19, 98-102.
Crowder, S. V., (1987b). Average run lengths of exponentially weighted moving average control charts. Journal of Quality Technology, 19, 161-164.
Crowder, S.V., (1987c). A simple method for studying run length distributions of exponentially weighted moving average control charts. Technometrics, 29, 401-407.
Crowder, S.V., (1989). Design of exponentially weighted moving average schemes. Journal of Quality Technology, 21, 155-162.
Crowder, S.V., and Hamilton, M. D., (1992). An EWMA for monitoring a process standard deviation. Journal of Quality Technology, 24(1), 12-21.
Del Castillo, E., (1996a). Run length distributions and economic design of charts with unknown process variance. Metrika, 43, 189-201.
Del Castillo, E., (1996b). Evaluation of run length distribution for charts with unknown variance. Journal of Quality Technology, 28, 116-122.
Del Castillo, E., (2002). Statistical Process Adjustment for Quality Control. John Wiley & Sons, New York.
DeVor, R. E., Chang, T. H., and Sutherland J. W., (1992) Statistical Quality Design and Control., Macmillan, New York.
Domangue R., and Patch, S. C., (1991). Some omnibus exponentially weighted moving averages statistical process monitoring schemes. Technometrics, 33(3), 299-313.
Duncan, A. J., (1986). Quality Control and Industrial Statistics, Fifth Edition., Irwin, Homewood Illinois.
Gan, F. F., (1991). Computing the percentage points of the run length distribution of an exponentially weighted moving average control chart. Journal of Quality Technology, 23, 359-365.
Gan, F. F., (1995). Joint monitoring of process mean and variance using exponentially weighted moving average control charts. Technometrics, 37(4), 446-453.
Gitlow, H., Oppenheim, A. and R. Oppenheim, (1995). Quality Management: Tools and Methods for Improvement, Second Edition. Irwin, Burr Ridge, Illinois.
Grant, E. L., and Leavenworth, R. S., (1988).Statistical Quality Control. Mcgraw-Hill, New York.
Hamilton, M. D., Crowder, S. V., (1992). Average run lengths of EWMA control charts for monitoring a process standard deviation. Journal of Quality Technology; 24(1), 44-50.
Hunter, J. S., (1986). The exponentially weighted moving average. Journal of Quality Technology, 18, 203-210.
IMSL (1989). User’s Manual Statistical Library Version 1.1. IMSL Inc: Houston, TX.
Jones, L. A., Champ C. W., and Rigdon S. E., (2001). The performance of exponentially weighted moving average charts with estimated parameters. Technometrics, 43, 156-167.
Klein, M., (1996). Composite Shewhart-EWMA statistical control schemes. IIE Transactions, 28, 475-481.
Klein, M., (1997). Modified Shewhart-exponentially weighted moving average control charts. IIE Transactions, 29, 1051-1056.
Klein, M., (2000). Two alternatives to the Shewhart control chart. Journal of Quality Technology, 32, 427-431.
Lucas, J. M., and Saccucci M. S., (1990). Exponential weighted moving average control schemes: properties and enhancements. Technometrics, 32, 1-12.
McGregor, F., and Harris J., (1993). The exponential weighted moving variance. Journal of Quality Technology, 25(2) ,106-118.
Mitra, A., (1993). Fundamentals of Quality Control and Improvement. Macmillan, New York.
Montgomery, D. C., (2001). Introduction to Statistical Quality Control (4th edn). John Wiley & Sons, New York.
Nelson, L. S., (1984). The Shewhart control chart-tests for special causes. Journal of Quality Technology, 16, 237-239.
Ng, C. H., and Case, K. E.,(1989). Development and evaluation of control charts using exponentially weighted moving averages. Journal of Quality Technology; 21(4), 242-250.
Quesenberry, C. P., (1993). The effect of sample size on estimated limits for and X control charts. Journal of Quality Technology; 25, 237-247.
Reynolds, M. R., Stoumbos, Z.G., (2001). Monitoring the process mean and variance using individual observations and variable sampling intervals. Journal of Quality Technology, 33(2), 181-205.
Reynolds, M. R., Stoumbos, Z.G., (2004).Control charts and the efficient allocation of sampling resources. Technometrics, 46(2), 200-214.
Rigdon, S.E., Curthis E.N., Chamo C.W., (1994). Design strategies for individuals and moving range control charts. Journal of Quality Technology, 26, 274-287.
Roberts, S. W., (1959). Control chart tests based on geometric moving averages. Technometrics, 1, 239-250.
Roberts, S. W., (1966). A comparison of some control chart procedures. Technometrics, 8, 411-430.
Robinson, P. B. and Ho, T. Y., (1978). Average run lengths of geometric moving average charts by numerical methods. Technometrics, 20, 85-93.
Saccucci, M. S., Lucas, J. M., (1990). Average run lengths for exponentially weighted moving average control schemes using the Markov chain approach. Journal of Quality Technology, 22, 154-162.
Shamma, S. E., Amin R. W., (1993). An EWMA quality control procedure for jointly monitoring the mean and variance. International Journal of Quality & Reliability Management, 10(7), 58-67.
Shea, G., (1993). Case study: simplicity in using Lab tests to check process analyzers. Process Control and Quality, (5), 123-130.
Sheu, S. H., Griffith W. S., (1996). Optimal number of minimal repairs before replacement of a system subject to shocks. Naval Research Logistics, 43, 319-333.
Sheu, S. H., (1998). A generalized age and block replacement of a system subject to shocks. European Journal of Operational Research, 108, 345-362.
Sheu, S. H., (1999). Extended optimal replacement model for deteriorating systems. European Journal of Operational Research, 112, 503-516.
Sheu, S. H., Lin T. C., (2003). The generally weighted moving average control chart for detecting small shifts in the process mean. Quality Engineering, 16(2), 209-231.
Steiner, S. H., (1999). EWMA control charts with time-varying control limits and fast initial response. Journal of Quality Technology, 31, 75-86.
Sweet, A. L., (1986). Control charts using coupled exponential weighted moving average. IIE Transactions, 18, 26-33.
Vance, L. C., (1983). A bibliography of statistical quality control chart techniques, 1970-1980. Journal of Quality Technology, 15(2), 59-62.
Wortham, A. W., and Ringer, L. J.,(1971). Control via exponential smoothing. The Logistic Review, 7(32), 33-40.
Wortham, A. W., and Heinrich, G. F.,(1972). Control charts using exponential smoothing techniques. Annual Technical Conference, Transactions of the American Society for Quality Control 26,451-458.