在現代製造業中，多變量管制圖已被廣泛應用於檢測製程異常。然而，它卻無法直接辨識異常來源，這是製程監控中的一大挑戰。因此，本研究旨在發展一套有效且即時的方法，以應對製造過程中的維度災難，同時識別多變量製程中的異常來源，提高監控的準確性和效率。
資料前處理採用B4-Broken-stick變數選擇方法，有效降低多維度數據的複雜性。本研究使用基於Model-Agnostic Meta-Learning方法的深度神經網路進行異常來源的分類。實驗結果顯示，本研究提出的 MAML of DNNs 模型透過少量樣本學習，快速適應新任務，在不同偏移情況下能夠有效處理所有異常狀況並保持良好的準確率。與 MLP 模型相比，MAML of DNNs 模型在準確率和訓練時間上均表現較佳，證實其在識別多變量製程異常來源方面更具效率和效果。將MAML of DNNs模型應用於生產過程中，可以即時辨識異常來源，幫助相關領域人員更有效率和高效地進行品質改善工作。

In modern manufacturing, multivariate control charts have been widely used to detect process anomalies. However, they cannot directly identify the source of out-of-control signals, posing a significant challenge in process monitoring. This study aims to develop an effective and real-time method to address the curse of dimensionality in manufacturing processes while identifying the source of out-of-control signals in multivariate processes, thereby improving monitoring accuracy and efficiency.
This study employs the B4-Broken-stick variable selection method to effectively reduce the complexity of high-dimensional data. We propose using a deep neural network based on Model-Agnostic Meta-Learning (MAML) to classify the sources of out-of-control signals. Experimental results show that the proposed MAML of DNNs model learns from a small number of samples and quickly adapts to new tasks, effectively handling all anomaly conditions and maintaining high accuracy under various shift scenarios. Compared to the MLP model, the MAML of DNNs model performs better in both accuracy and training time, demonstrating its efficiency and effectiveness in identifying the sources of out-of-control signals in multivariate processes. Applying the MAML of DNNs model in the production process enables real-time identification of the sources of out-of-control signals, assisting personnel in related fields to conduct quality improvement work more efficiently and effectively.

[1] Abdi, H., & L. J. Williams. "Principal component analysis." Wiley Interdisciplinary Reviews: Computational Statistics 2.4, 2010, 433-459.
[2] Aslam, M., A. Saghir, & L. Ahmad. Introduction to Statistical Process Control. John Wiley & Sons, 2020.
[3] Bersimis, S., S. Psarakis, & J. Panaretos. "Multivariate statistical process control charts: an overview." Quality and Reliability Engineering International 23.5, 2007, 517-543.
[4] Chen, L. H., & T. Y. Wang. "Artificial neural networks to classify mean shifts from multivariate χ2 chart signals." Computers & Industrial Engineering 47.2-3, 2004, 195-205.
[5] Cheng, C. S. "A multi-layer neural network model for detecting changes in the process mean." Computers & Industrial Engineering 28.1, 1995, 51-61.
[6] Cheng, C. S., & H. T. Lee. "Diagnosing the variance shifts signal in multivariate process control using ensemble classifiers." Journal of the Chinese Institute of Engineers 39.1, 2016, 64-73.
[7] Diren, D. D., S. Boran, & I. Cil. "Integration of machine learning techniques and control charts in multivariate processes.", 2020.
[8] Doganaksoy, N., F. W. Faltin, & W. T. Tucker. "Identification of out of control quality characteristics in a multivariate manufacturing environment."
Communications in Statistics-Theory and Methods 20.9, 1991, 2775-2790.
[9] Finn, C., P. Abbeel, & S. Levine. "Model-agnostic meta-learning for fast adaptation of deep networks." International Conference on Machine Learning. PMLR, 2017, 1126-1135.

[10] Frontier, S. "Étude de la décroissance des valeurs propres dans une analyse en composantes principales: Comparaison avec le modd́le du bâton brisé." Journal of Experimental Marine Biology and Ecology 25.1, 1976, 67-75.
[11] Guh, R. S., & Y. R. Shiue. "An effective application of decision tree learning for on-line detection of mean shifts in multivariate control charts." Computers & Industrial Engineering 55.2, 2008, 475-493.
[12] Guo, Y., & K. J. Dooley. "Identification of change structure in statistical process control." The International Journal of Production Research 30.7, 1992, 1655-1669.
[13] Hawkins, D. M. "Multivariate quality control based on regression-adiusted variables." Technometrics 33.1, 1991, 61-75.
[14] Hawkins, D. M. "Regression adjustment for variables in multivariate quality control." Journal of Quality Technology 25.3, 1993, 170-182.
[15] Hayter, A. J., & K. L. Tsui. "Identification and quantification in multivariate quality control problems." Journal of Quality Technology 26.3, 1994, 197-208.
[16] Jackson, D. A. "Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches." Ecology 74.8, 1993, 2204-2214.
[17] Jackson, J. E. "Multivariate quality control." Communications in Statistics-Theory and Methods 14.11, 1985, 2657-2688.
[18] Jolliffe, I. T. "Discarding variables in a principal component analysis. I: Artificial data." Journal of the Royal Statistical Society Series C: Applied Statistics 21.2, 1972, 160-173.
[19] King, J. R., & D. A. Jackson. "Variable selection in large environmental data sets using principal components analysis." Environmetrics: The Official Journal of the International Environmetrics Society 10.1, 1999, 67-77.

[20] Krenker, A., J. Bešter, & A. Kos. "Introduction to the artificial neural networks."
Artificial Neural Networks: Methodological Advances and Biomedical Applications. InTech, 2011, 1-18.
[21] Mason, R. L., N. D. Tracy, & J. C. Young. "Decomposition of T 2 for multivariate control chart interpretation." Journal of Quality Technology 27.2, 1995, 99-108.
[22] Montgomery, D. C. Introduction to Statistical Quality Control. John Wiley & Sons, 2019.
[23] Murphy, B. J. "Selecting out of control variables with the T2 multivariate quality control procedure." Journal of the Royal Statistical Society Series D: The Statistician 36.5, 1987, 571-581.
[24] Navamani, T. M. "Efficient deep learning approaches for health informatics."
Deep Learning and Parallel Computing Environment for Bioengineering Systems. Academic Press, 2019, 123-137.
[25] Niaki, S. T. A., & B. Abbasi. "Fault diagnosis in multivariate control charts using artificial neural networks." Quality and Reliability Engineering International
21.8, 2005, 825-840.
[26] Noorossana, R., M. Farrokhi, & A. Saghaei. "Using neural networks to detect and classify out‐of‐control signals in autocorrelated processes." Quality and Reliability Engineering International 19.6, 2003, 493-504.
[27] Psarakis, S. "The use of neural networks in statistical process control charts."
Quality and Reliability Engineering International 27.5, 2011, 641-650.
[28] Song, H., Q. Xu, H. Yang, & J. Fang. "Interpreting out-of-control signals using instance-based Bayesian classifier in multivariate statistical process control."
Communications in Statistics-Simulation and Computation 46.1, 2017, 53-77.
[29] Vanschoren, J. "Meta-learning: A survey." arXiv preprint arXiv:1810.03548, 2018.

[30] Western Electric Company. Statistical Quality Control Handbook. AT & T Technologies, 1958.
[31] Wold, S., K. Esbensen, & P. Geladi. "Principal component analysis."
Chemometrics and Intelligent Laboratory Systems 2.1-3, 1987, 37-52.
[32] Yu, J., L. Xi, & X. Zhou. "Identifying source (s) of out-of-control signals in multivariate manufacturing processes using selective neural network ensemble."
Engineering Applications of Artificial Intelligence 22.1, 2009, 141-152.
[33] Zorriassatine, F., & J. D. T. Tannock. "A review of neural networks for statistical process control." Journal of Intelligent Manufacturing 9, 1998, 209-224.