在競爭激烈的製造市場中，為了提升競企業競爭力，品質管理也漸漸受到重視，因此各企業會使用不同的手法及工具監控製程的穩定性，統計製程管制圖是品質管理中常用的工具之一，用來偵測在生產時是否有變異發生。傳統修華特管制圖是由修華特博士在1931年發表，適用在監控較大的位移，後續漸漸發展出其他管制圖，像是累積和管制圖、指數加權移動管制圖等時間加權管制圖，可以針對特定位移進行最佳化的參數設定，在較小位移時也能有良好的偵測效果。
本研究希望透過資訊理論之Kullback-Leibler distance概念設計一個能監控廣泛位移且不需針對特定位移設定參數的管制圖(Information-theoretical Control Chart based on Geometric distribution)又稱ITG管制圖，並將不合格率分為三種情況分別為0.1、0.01、0.001下討論，並使用兩種方法計算Kullback-Leibler distance，第一種為使用Change point model找出可能發生位移的樣本位置並估計不合格率，第二種是由製程最後依序往前增加樣本個數估計其不合格率。
本研究透過幾何分佈產生亂數並進行蒙地卡羅模擬十萬次，將估計出的偵測能力與Bernoulli GLR管制圖、Bernoulli CUSUM做比較，透過結果分析後可以得知在使用由製程最後一期依序往前增加期數估計不合格率的方式計算Kullback-Leibler distance的方式在三種不合格率的設定下，廣泛位移中都有不錯的監控效果。而使用Change point model找出可能發生位移的樣本位置並估計不合格率方法的表現則是與不合格率的大小有關，在不合格率為0.01及0.001時表現較好，在不合格率為0.1時表現較差。

The control chart of this study considers a process when all inspected items can be classified into two categories: conforming and nonconforming. The study objective is to effectively detect a wide range of increasing in the nonconforming rate p. The methodology is based on Kullback-Leibler distance of information theory, which measures the information discrepancy of two distributions. We name this control chart Information-theoretical Control Chart Based on Geometric Distribution (ITG control chart). This study uses two approaches to construct the ITG control chart, maximum-likelihood method and backward sequential chi-square test, respectively. We call that ITG-L chart and ITG-I chart. The Phase Ⅱ performance of this chart in detecting sustained increases in p is evaluated by the average number of observations to signal (ANOS). Comparisons of the Bernoulli GLR chart, the Bernoulli cumulative sum chart, and the Bernoulli exponentially weighted moving average chart are presented. The ITG control chart using maximum likelihood method seems better in detecting nonconforming rate is 0.01 and 0.001. By contrast, backward sequential chi-square test shows that the overall performance of the ITG control chart is better than its competitors. It is effective in detecting wide range shift.

中文文獻：
劉英守，應用資訊理論於監控伯努力過程之管制圖，國立成功大學工業與資訊管理研究所碩士論文，民國一百零四年六月。
英文文獻：
Akaike, H. (1974). A new look at the statistical model identification. Automatic Control, IEEE Transactions on, 19(6), 716-723.
Bourke, P. D. (1991). Detecting a shift in fraction nonconforming using run-length control charts with 100% inspection. Journal of Quality Technology,23(3), 225-238.
Burnham, K. P. & Anderson, D. R. (2001). Kullback-Leibler information as a basis for strong inference in ecological studies. Wildlife research, 28(2), 111-119.
Do, M. N. & Vetterli, M. (2000). Texture similarity measurement using Kullback-Leibler distance on wavelet subbands. In Image Processing, 2000 Proceedings. 2000 International Conference on (Vol. 3, pp. 730-733). IEEE.
Gokhale, D. & Kullback, S. (1978). The information in contingency tables.
Hawkins, D. M., Qiu, P. & Kang, C. W. (2003). The changepoint model for statisticalprocess control. Journal of quality technology, 35(4), 355-366.
Huang, W., Wang, S.& Reynolds, M. R. (2013). A generalized likelihood ratio chart for monitoring Bernoulli processes. Quality and Reliability Engineering International, 29(5), 665-679.
Hunter, J. S. (1986). The exponentially weighted moving average. J. Quality Technol.,18(4), 203-210.
Goh, T. N. (1987). A control chart for very high yield processes. Quality Assurance,13(1), 18-22.
Kanagawa A., Arizono, I. & Ohta H. (1997). Design of the control chart based on Kullback-Leibler information. Frontiers in Statistical Quality Control, 5, 183-192.
Kullback, S. & Leibler, R. A. (1951). On information and sufficiency. The annals of mathematical statistics, 79-86.
Lucas, J. M. & Crosier, R. B. (1982). Fast initial response for CUSUM quality-control schemes: give your CUSUM a head start. Technometrics, 24(3), 199-205.
Montgomery, D. C. (2009). Statistical Quality Control-A Modern Introduction, John Whiley & Sons. New York.
Page, E. S. (1954). Continuous inspection schemes. Biometrika, 100-115.
Pan, W. (2001). Akaike's information criterion in generalized estimating equations. Biometrics, 57(1), 120-125.
Park, S. (2005). Testing exponentiality based on the Kullback-Leibler information with the type II censored data. Reliability, IEEE Transactions on, 54(1), 22-26.
Reynolds Jr, M. R. & Stoumbos, Z. G. (1999). A CUSUM chart for monitoring a proportion when inspecting continuously. Journal of Quality Technology, 31(1), 87.
Reynolds Jr, M. R., & Lou, J. (2010). An evaluation of a GLR control chart for monitoring the process mean. Journal of quality technology, 42(3), 287.
Reynolds Jr, M. R., Lou, J., Lee, J., & Wang, S. (2013). The design of GLR control charts for monitoring the process mean and variance. Journal of Quality Technology, 45(1), 34.
Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(3), 239-250.
Roberts, S. W. (1966). A comparison of some control chart procedures. Technometrics, 8(3), 411-430.
Ryan, T. P. & Schwertman, N. C. (1997). Optimal limits for attributes control charts. Journal of Quality Technology, 29(1), 86.
Szarka, J. L. & Woodall, W. H. (2011). A review and perspective on surveillance of Bernoulli processes. Quality and Reliability Engineering International, 27(6), 735-752.
Woodall, W. H. (1997). Control charts based on attribute data: bibliography and review. Journal of quality technology, 29(2), 172.
Zamba, K. D. & Hawkins, D. M. (2005). Statistical Process Control for Shifts in Mean or Variance Using a Changepoint Formulation. Technometrics, (2), 164-173.
Zhao, Y., Tsung, F. & Wang, Z. (2005). Dual CUSUM control schemes for detecting a range of mean shifts. IIE transactions, 37(11), 1047-1057.