CUSUM管制圖為統計製程管制中重要的工具之一，當製程偏移量為已知時，將能夠進行CUSUM管制圖的最佳化設計，對於製程平均數發生中、小幅度偏移具有良好的表現。然而在現實中並無法事先取得製程的偏移量，因而使得CUSUM管制圖的偵測能力降低。許多學者提出多重管制圖、適應性管制圖、配飾偏移量機率分配等技術來處理此問題，然而多重管制圖若結合管制圖的數量太多將會造成設計困難，而適應性管制圖可能會因變換管制參數頻率過高而導致管理成本增加，而隨後提出的配適偏移量機率分配解決了上述兩種技術的問題，但並未善用過去製程偏移量資訊，可能會與實際情況產生誤差，進而影響累積和管制圖的表現。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，除此之外，因二次損失函數不僅將所有製程資訊納入考量，也包含成本損失的評估，故本研究將利用類神經網路配適製程偏移量機率分配及參數，並以二次損失函數為基礎建構CUSUM管制圖參數設計模式以最佳化管制參數進而建立最小化EQL之累積和管制圖，不僅克服之前研究中人為配適所造成的風險，更能體現使用管制圖所帶來的效益。經由本研究所設計的模擬情境對管制圖進行分析，發現當偏移量之機率分配不相符以及偏移量之機率分配參數與實際參數具有正負向的落差，最小化EQL之累積和管制圖能夠改善偵測中小幅度偏移效率不佳的問題，並加速大偏移的偵測效率，然而當實際偏移量服從均勻分配時，改善偵測能力的幅度較不明顯。最後，本研究利用前人研究所記錄的品質特性資料來進一步來評估最小化EQL之累積和管制圖相對於其他採用不同方式設計的累積和管制圖的表現，發現最小化EQL之累積和管制圖的偵測效率至少能夠達到相同水平，甚至較其他管制圖來的好。

The cumulative sum (CUSUM) control chart has been widely used in statistical process (SPC) across industries for monitoring process mean shift. When one specific size of the mean shift is assumed, the CUSUM chart can be optimally designed in terms of average run length (ARL). In practice, however, the shift size is usually unknown, and the CUSUM chart can perform poorly when the actual mean shift size is significantly different form the assumed size. Most researchers directly assume or assign a particular probability distribution to the size of the mean shift to represent the lack of knowledge of the shift size. However, this method is risky because real probability distribution of shift size may be different from the user-assigned distribution. In this study, we propose a mechanism based on applying support vector machine (SVM) regression to the distribution fitting of the shift size. We find the parameter of the chart by minimizing the Taguchi-base function, called extra quadratic loss (EQL) function. EQL is used to evaluate the expected loss due to poor quality. In addition, this design decreases the risk that user directly assign distribution of the shift size and corresponds with the need of the enterprise because the EQL-CUSUM chart provides expected cost to the decision maker. Finally, the simulation study and the real data from the previous researcher are used to demonstrate the effectiveness of the proposed EQL-CUSUM chart.

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 influence of reference values and estimated variance on the ARL of CUSUM tests. Journal of the Royal Statistical Society, 37(3), 413-420.

Chang, C.-C., & Lin, C.-J. (2011). LIBSVM: A Library for Support Vector Machines. ACM Transactions on Intelligent Systems and Technology, 2(3).

Chen, A., & Chen, Y. K. (2007). Design of EWMA and CUSUM control charts subject to random shift sizes and quality impacts. IIE Transactions, 39(12), 1127-1141.

Cheng, C.-S., Chen, P.-W., & Huang, K.-K. (2011). Estimating the shift size in the process mean with support vector regression and neural networks. Expert Systems with Applications, 38(8), 10624-10630.

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.

Cherkassky, V., & Ma, Y. Q. (2004). Practical selection of SVM parameters and noise estimation for SVM regression. Neural Networks, 17(1), 113-126.

Cherkassky, V. S., & Mulier, F. (1998). Learning from Data: Concepts, Theory, and Methods: New York: Wiley.

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.

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.

Han, D., & Tsung, F. G. (2006). A reference-free Cuscore chart for dynamic mean change detection and a unified framework for charting performance comparison. Journal of the American Statistical Association, 101(473), 368-386.

Hawkins, D. M. (1987). Self-starting CUSUM charts for location and scale. Statistician, 36(4), 299-315.

Hyu, O.-H., Wan, H., & Kim, S. (2010). Optimal design of a CUSUM chart for a mean shift of unknown size. Journal of Quality Technology, 42(3), 311-326.

Jiang, W., Shu, L., & Apley, D. W. (2008). Adaptive CUSUM procedures with EWMA-based shift estimators. IIE Transactions, 40(10), 992-1003.

Jiao, J. R., & Helo, P. T. (2008). Optimization design of a CUSUM control chart based on taguchi's loss function. International Journal of Advanced Manufacturing Technology, 35(11-12), 1234-1243.

Kwok, J. (2001). Linear dependency between ε and the input noise in ε-support vector regression. In G. Dorffner, H. Bischof & K. Hornik (Eds.), Artificial Neural Networks — ICANN 2001 (pp. 405-410). Berlin: Springer.

Lucas, J. M. (1982). Combined Shewhart-CUSUM quality control schemes. Journal of Quality Technology, 14(2), 51-59.

Luo, Y., Li, Z., & Wang, Z. (2009). Adaptive CUSUM control chart with variable sampling intervals. Computational Statistics & Data Analysis, 53(7), 2693-2701.

Mattera, D., & Haykin, S. (1999). Support vector machines for dynamic reconstruction of a chaotic system. In S. Bernhard, lkopf, J. C. B. Christopher & J. S. Alexander (Eds.), Advances in kernel methods (pp. 211-241): MIT Press.

Montgomery, D. C. (2012). Statistical Quality Control: A Modern Introduction. New York: Wiley.

Moustakides, G. V. (1986). Optimal stopping times for detecting changes in distributions. Annals of Statistics, 14(4), 1379-1387.

Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1-2), 100-115.

Reynolds, M. R., Amin, R. W., & Arnold, J. C. (1990). CUSUM charts with variable sampling intervals. Technometrics, 32(4), 371-384.

Ross, P. J. (1996). Taguchi Techniques for Quality Engineering: Loss Function, Orthogonal Experiments, Parameter and Tolerance Design. New York: McGraw-Hill.

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.

Schèolkopf, B., Burges, C. J. C., & Smola, A. J. (1999). Advances in kernel methods : Support vector learning. Cambridge, Mass: MIT Press.

Shu, L., Jiang, W., & Tsui, K.-L. (2008). A weighted CUSUM chart for detecting patterned mean shifts. Journal of Quality Technology, 40(2), 194-213.

 
Shu, L. J., & Jiang, W. (2006). A Markov chain model for the adaptive CUSUM control chart. Journal of Quality Technology, 38(2), 135-147.

Siegmund, D. (1985). Sequential analysis: tests and confidence intervals. New York: Springer-Verlag.
Smola, A. J., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and computing, 14(3), 199-222.

Sparks, R. S. (2000). CUSUM charts for signalling varying location shifts. Journal of Quality Technology, 32(2), 157-171.

Sun, R. X., & Tsung, F. (2003). A kernel-distance-based multivariate control chart using support vector methods. International Journal of Production Research, 41(13), 2975-2989.

Tagaras, G. (1998). A survey of recent developments in the design of adaptive control charts. Journal of Quality Technology, 30(3), 212-231.

Vapnik, V. N. (1995). The nature of statistical learning theory. New York: Springer-Verlag.

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., Yang, M., Khoo, M. B. C., & Yu, F.-J. (2010). Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance. European Journal of Operational Research, 205(1), 136-150.

Zhang, C., Tsung, F., & Zou, C. (2015). A general framework for monitoring complex processes with both in-control and out-of-control information. Computers & Industrial Engineering, 85, 157-168.
 
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.