管制圖為現今企業常用來監控製程的一項工具，其中CUSUM管制圖為管制圖的代表之一，對於製程平均中微小的偏移較為靈敏，而後，學者針對累積和管制圖做出改良，提出了ACUSUM管制圖，相較於CUSUM管制圖，ACUSUM管制圖根據製程偏移量的估計值來調整參數，透過調整參數，可實現比傳統CUSUM圖更好的性能。但ACUSUM管制圖僅根據上期資訊決定參數大小，對於過去歷史製程偏移量的資訊並無善加利用，可能會與實際的情況產生誤差，影響到ACUSUM管制圖的效能，並且目前對於計算ACUSUM統計量的方式也眾說紛紜，並無一個明確的標準。類神經網路具有高容量的學習能力，適用於分類及預測的問題上，且應用於管制圖也有良好的表現，可針對過去歷史資料進行訓練，找出其關聯性。本研究主要利用類神經網路訓練ACUSUM管制圖中所使用之權重，透過過往的歷史資料和相關參數，找出其對應的權重大小為何，同時與其他方法進行比較。結果顯示DNN在五種方法中擁有最好的績效，接著並透過DNN訓練出之最佳參數，建構ACUSUM管制圖，並且帶入不同的製程資料，直到ACUSUM統計量超出上限，找出其對應之ARL長度大小，並與其餘管制圖進行比較。結果顯示不論是在常態分配或指數分配下，在小偏移製程時，本研究所提出的改良式之適應性累積和管制圖可以較快速的偵測到異常發生；在大偏移製程時，雖然不同的管制圖都可以快速偵測到異常，但本研究所提出之適應性累積和管制圖仍具有相對的優勢。

Control charts are commonly used tools in today's businesses for monitoring processes. Among them, scholars have made improvements to the cumulative sum (CUSUM) control chart and proposed the Adaptive CUSUM (ACUSUM) control chart. ACUSUM control chart adjusts its parameters based on the assumed process shift. However, the ACUSUM control chart only determines the parameter size based on the previous information, without effectively utilizing the historical information. This lack of utilization of historical information may lead to errors and impact the performance. Neural networks possess high learning capacity and are suitable for prediction problems. In this study, we mainly used a neural network to train the weights used in the ACUSUM control chart. Through historical data, we determined the appropriate weight values. We compared the results with other methods and showed that the Deep Neural Network (DNN) had the best performance among the five methods. Then, we used the trained DNN to construct the ACUSUM control chart and applied it to different data. We observed the occurrence of anomalies when the ACUSUM statistic exceeded the upper limit and determined the corresponding Average Run Length (ARL). We compared the results with other control charts. The findings showed that no matter the process followed a normal distribution or an exponential distribution, the proposed adaptive ACUSUM control chart in this study could detect anomalies more quickly in small shift processes. In large shift processes, although different control charts could detect anomalies rapidly, the adaptive ACUSUM control chart proposed in this study still demonstrated relative advantages.

Abbasi, S., & Haq, A. (2019). Optimal CUSUM and adaptive CUSUM charts with auxiliary information for process mean. Journal of Statistical Computation and Simulation, 89(2), 337-361.
Altman, N. S. (1992). An introduction to kernel and nearest-neighbor nonparametric regression. The American Statistician, 46(3), 175-185.
Annadi, H. P., Keats, J. B., Runger, G. C., & Montgomery, D. C. (1995). An adaptive sample size CUSUM control chart. International Journal of Production Research, 33(6), 1605-1616.
Arnold, J. C., & Reynolds, M. R. (2001). CUSUM control charts with variable sample sizes and sampling intervals. Journal of Quality Technology, 33(1), 66-81.
Bagshaw, M., & Johnson, R. A. (1975). The effect of serial correlation on the performance of CUSUM tests II. Technometrics, 17(1), 73-80.
Breiman, L. (2001). Random forests. Machine learning, 45(1), 5-32.
Breiman, L., Friedman, J., Stone, C. J., & Olshen, R. A. (1984). Classification and Regression Trees. Taylor & Francis Group.
Chang, S. I. and Aw, C. A. (1996). A neural fuzzy control chart for detecting and classifying process mean shifts. International Journal of Production Research, 34(8), 2265-2278.
Chen, L. H. and Wang, T. Y. (2004). Artificial neural networks to classify mean shifts from multivariate χ2 chart signals. Computers & Industrial Engineering, 47(2-3), 195-205.
Cheng, C. S. (1994). Detecting changes in the process mean using artificial neural networks approach. Journal of Chinese Institute of Industrial Engineers, 11, 47-54.
Cheng, C. S., & Cheng, H. P. (2008). Identifying the source of variance shifts in the multivariate process using neural networks and support vector machines. Expert Systems with Applications, 35(1-2), 198-206.
Cheng, C. S. & Cheng, S. S. (2001). A neural-based procedure for the monitoring of exponential mean. Computers & Industrial Engineering, 40, 309-321.
Chinnam, R. B. (2002). Support vector machines for recognizing shifts in correlated and other manufacturing processes. International Journal of Production Research, 40(17), 4449-4466.
Dragalin, V. (1997). The design and analysis of 2-CUSUM procedure. Communications in Statistics-Simulation and Computation, 26(1), 67-81.
Du, S., Lv, J., & Xi, L. (2012). On-line classifying process mean shifts in multivariate control charts based on multiclass support vector machines. International Journal of Production Research, 50(22), 6288-6310.
El-Midany, T. T., El-Baz, M. A. and Abd-Elwahed, M. S. (2010). A proposed framework for control chart pattern recognition in multivariate process using artificial neural networks. Expert Systems with Applications, 37(2), 1035-1042.
Georganos, S., Grippa, T., Vanhuysse, S., Lennert, M., Shimoni, M., Kalogirou, S., & Wolff, E. (2018). Less is more: optimizing classification performance through feature selection in a very-high-resolution remote sensing object-based urban application. GIScience & Remote Sensing, 55(2), 221-242.
Han, D., Tsung, F., Hu, X., & Wang, K. (2007). CUSUM and EWMA multi-charts for detecting a range of mean shifts. Statistica Sinica, 17(3), 1139-1164.
Hsu, C. W., Chang, C. C., & Lin, C. J. (2003). A practical guide to support vector classification, Technical Report, Issue.
Jiang, W., Shu, L., & Apley, D. W. (2008). Adaptive CUSUM procedures with EWMA-based shift estimators. IIE Transactions, 40(10), 992-1003.
Kim, J., Al-Khalifa, K. N., Park, M., Jeong, M. K., Hamouda, A. M. S., & Elsayed, E. A. (2013). Adaptive cumulative sum charts with the adaptive runs rule. International Journal of Production Research, 51(15), 4556-4569.
Kumar, S. (2004). Neural Networks a classroom approach. tata Mc Graw Hill. Liu, L., Chen, B., Zhang, J., & Zi, X. (2015). Adaptive phase II nonparametric EWMA control chart with variable sampling interval. Quality and Reliability Engineering International, 31(1), 15-26.
Luo, Y., Li, Z., & Wang, Z. (2009). Adaptive CUSUM control chart with variable sampling intervals. Computational Statistics & Data Analysis, 53(7), 2693-2701.
Lucas, J. M. (1982). Combined Shewhart-CUSUM quality control schemes. Journal of Quality Technology, 14(2), 51-59.
Montgomery, D. C. (2012). Statistical Quality Control: A Modern Introduction. NewYork: Wiley.
Moustakides, G. V. (1986). Optimal stopping times for detecting changes in distributions. Annals of Statistics, 14(4), 1379-1387.
Nair, V., & Hinton, G. E. (2010). Rectified linear units improve restricted boltzmann machines. Proceedings of the 27th International Conference on Machine Learning (ICML-10) (pp.807-814).
Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100-115.
Patel, H., Thakkar, A., Pandya, M., & Makwana, K. (2018). Neural network with deep learning architectures. Journal of Information and Optimization Sciences, 39(1), 31-38.
Psarakis, S. (2011). The use of neural networks in statistical process control charts. Quality and Reliability Engineering International, 27(5), 641-650.
Pugh, G. A. (1989). Synthetic neural networks for process control. Computers and Industrial Engineering, 17, 24-26.
Quinlan, J. R. (1986). Induction of decision trees. Machine learning, 1, 81-106.
Rosenblatt, F. (1958). The perceptron: a probabilistic model for information storage and organization in the brain. Psychological Review, 65(6), 386.
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323(6088), 533-536.
Salehi, M., Kazemzadeh, R. B., & Salmasnia, A. (2012). On line detection of mean and variance shift using neural networks and support vector machine in multivariate processes. Applied Soft Computing, 12(9), 2973-2984.
Scholkopf, B., Sung, K.-K., Burges, C. J., Girosi, F., Niyogi, P., Poggio, T., & Vapnik, V.(1997). Comparing support vector machines with Gaussian kernels to radial basis function classifiers. IEEE Transactions on Signal Processing, 45(11), 2758-2765.
Shu, L., & Jiang, W. (2006). A Markov chain model for the adaptive CUSUM control chart. Journal of Quality Technology, 38(2), 135-147.
Sparks, R. S. (2000). CUSUM charts for signaling varying location shifts. Journal of Quality Technology, 32(2), 157-171.
Sun, R. and Tsung, F. (2003). A kernel-distance-based multivariate control chart using support vector methods. International Journal of Production Research, 41, 2975-2989.
Timofeev, R. (2004). Classification and regression trees (CART) theory and applications. Humboldt University, Berlin, 54.
Vapnik, V. N. (1995). The nature of statistical learning theory. New York: Springer-Verlag.
Wang, T. Y. and Chen, L. H. (2002). Mean shifts detection and classification in multivariate process: a neural-fuzzy approach. Journal of Intelligent Manufacturing, 13(3), 211-221.
Wu, C., Liu, F. & Zhu, B. (2015). Control chart pattern recognition using an integrated model based on binary-tree support vector machine. International Journal of Production Research, 53(7), 2026-2040.
Wu, Z., Jiao, J., Yang, M., Liu, Y., & Wang, Z. (2009). An enhanced adaptive CUSUM control chart. IIE Transactions, 41(7), 642-653.
Yu, J. B. and Xi, L. F. (2009). A neural network ensemble-based model for on-line monitoring and diagnosis of out of control signals in multivariate manufacturing processes. Expert Systems with Applications, 36, 909–921.
Zhao, Y., Tsung, F., & Wang, Z. J. (2005). Dual CUSUM control schemes for detecting a range of mean shifts. IIE Transactions, 37(11), 1047-1057.