為解決多變量和自相關製程管制之困難，本論文建立一種新穎的管制圖 AR-XkA。 本研究根據平均遊程 (ARL) 指標，並進行 AR-XkA 管制圖的表現與現有管制圖（即 CCCgroup 和 R-MMCE管制圖）之比較。研究結果顯示，AR-XkA 管制圖優於 CCCgroup 管制圖，特別是在 ARL1 的表現，顯示其對製程平均值變化的敏感度增強，尤其是對於變數 X1A。 然而，對於較大的 k 值（k ≥ 50），ARL0 接近 370，顯示檢測失控現象的表現下降。 與 R-MMCE 管制圖的比較分析顯示，對於較大的 k 值，AR-XkA管制圖在 ARL1 方面表現較差，但表現出與 CCCgroup 管制圖類似的性能。 值得注意的是，AR-XkA 管制圖因其採樣有效性而備受關注，使品質管理人員能夠簡化品質控制流程。本研究所提出的管制圖透過在 XkA 管制圖方案定義的周期內，實施屬性檢查以減少採樣時間。這種品質管制策略消除了在整個過程中進行連續變數檢查的需要，對於持續時間較長的製程尤其有利。

This dissertation introduces a novel control chart, the AR-XkA, designed to address challenges associated with multivariate and autocorrelated processes. The study evaluates the performance of the AR-XkA control chart in comparison to established charts, namely the CCCgroup and R-MMCE charts, based on the Average Run Length (ARL) metrics. Results indicate that the AR-XkA chart outperforms the CCCgroup chart, particularly in terms of ARL1, showcasing enhanced sensitivity to shifts in process mean, especially for the variable X1A. However, for larger values of k (k ≥ 50), ARL0 approaches 370, indicating a decrease in performance in detecting out-of-control conditions. Comparative analysis with the R-MMCE chart reveals that the AR-XkA chart performs worse in terms of ARL1 for larger k values but exhibits performance similar to the CCCgroup chart. Notably, the AR-XkA control chart is highlighted for its effectiveness in sampling, enabling operators to streamline the quality control process. The proposed control chart allows operators to reduce sampling time by implementing attribute inspections within cycles defined by the XkA control chart scheme. This strategic approach eliminates the need for continuous variable inspections throughout the entire process, particularly advantageous for processes with extended durations.

References
Ajadi, J. O., & Riaz, M. (2017). Mixed multivariate EWMA-CUSUM control charts for an improved process monitoring. Communications in Statistics - Theory and Methods, 46(14), 6980–6993. https://doi.org/10.1080/03610926.2016.1139132
Akram, M. W., Li, G., Jin, Y., Chen, X., Zhu, C., Zhao, X., Khaliq, A., Faheem, M., & Ahmad, A. (2019). CNN based automatic detection of photovoltaic cell defects in electroluminescence images. Energy, 189, 116319. https://doi.org/10.1016/j.energy.2019.116319
Ali, S., Pievatolo, A., & Göb, R. (2016). An Overview of Control Charts for High-quality Processes. Quality and Reliability Engineering International, 32(7), 2171–2189. https://doi.org/10.1002/qre.1957
Alwan, L. C., & Roberts, H. V. (1988). Time-Series Modeling for Statistical Process Control Time-Series Mode ing for Statistics Process Contro. Journal of Business & Economic Statistics, 6(1), 87–95. https://doi.org/http://dx.doi.org/10.1080/07350015.1988.10509640
Atienza, O. O., Tang, L. C., & Ang, B. W. (2002). A CUSUM scheme for autocorrelated observations. Journal of Quality Technology, 34(2), 187–199. https://doi.org/10.1080/00224065.2002.11980145
Calvin, T. W. (1983). Quality Control Techniques for “Zero Defects”. Technical Paper - Society of Manufacturing Engineers, C(3), 323–328. https://doi.org/10.1016/0026-2714(84)90075-1
Chen, H., & Cheng, Y. (2009). Designing over(X, -) charts for known autocorrelations and unknown marginal distribution. European Journal of Operational Research, 198(2), 520–529. https://doi.org/10.1016/j.ejor.2008.09.007
Chiang, J. Y., Lio, Y. L., & Tsai, T. R. (2017). MEWMA Control Chart and Process Capability Indices for Simple Linear Profiles with Within-profile Autocorrelation. In Quality and Reliability Engineering International (Vol. 33, Issue 5, pp. 1083–1094). https://doi.org/10.1002/qre.2101
Costa, A. F. B., & MacHado, M. A. G. (2011). Variable parameter and double sampling X̄ charts in the presence of correlation: The Markov chain approach. International Journal of Production Economics, 130(2), 224–229. https://doi.org/10.1016/j.ijpe.2010.12.021
Dai, W., Mujeeb, A., Erdt, M., & Sourin, A. (2020). Soldering defect detection in automatic optical inspection. Advanced Engineering Informatics, 43(November 2019), 101004. https://doi.org/10.1016/j.aei.2019.101004
Du, S., Huang, D., & Lv, J. (2013). Recognition of concurrent control chart patterns using wavelet transform decomposition and multiclass support vector machines. Computers and Industrial Engineering, 66(4), 683–695. https://doi.org/10.1016/j.cie.2013.09.012
Ebayyeh, A. A. R. M. A., & Mousavi, A. (2020). A Review and Analysis of Automatic Optical Inspection and Quality Monitoring Methods in Electronics Industry. IEEE Access, 8, 183192–183271. https://doi.org/10.1109/ACCESS.2020.3029127
ElMaraghy, H., Monostori, L., Schuh, G., & ElMaraghy, W. (2021). Evolution and future of manufacturing systems. CIRP Annals, 70(2), 635–658. https://doi.org/10.1016/j.cirp.2021.05.008
Elvira N. Loredo, D. J. & C. M. B. (2002). Model‐based control chart for autoregressive and correlated data.pdf. Quality and Reliability Engineering International, 18, 489–496.
Fallah Nezhad, M. S., & Akhavan Niaki, S. T. (2010). A new monitoring design for uni-variate statistical quality control charts. Information Sciences, 180(6), 1051–1059. https://doi.org/10.1016/j.ins.2009.11.033
Flores, M., Naya, S., Fernández-Casal, R., Zaragoza, S., Raña, P., & Tarrío-Saavedra, J. (2020). Constructing a control chart using functional data. Mathematics, 8(1), 1–26. https://doi.org/10.3390/math8010058
Franco, B. C., Celano, G., Castagliola, P., & Costa, A. F. B. (2014). Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies. International Journal of Production Economics, 151, 121–130. https://doi.org/10.1016/j.ijpe.2014.02.008
Franco, B. C., Costa, A. F. B., & MacHado, M. A. G. (2012). Economic-statistical design of the X chart used to control a wandering process mean using genetic algorithm. Expert Systems with Applications, 39(17), 12961–12967. https://doi.org/10.1016/j.eswa.2012.05.034
Haq, A., & Khoo, M. B. C. (2019). New adaptive EWMA control charts for monitoring univariate and multivariate coefficient of variation. Computers and Industrial Engineering, 131, 28–40. https://doi.org/10.1016/j.cie.2019.03.027
He, Z., Wang, Z., Tsung, F., & Shang, Y. (2016). A control scheme for autocorrelated bivariate binomial data. Computers and Industrial Engineering, 98, 350–359. https://doi.org/10.1016/j.cie.2016.06.001
Huang, S. H., & Pan, Y. C. (2015). Automated visual inspection in the semiconductor industry: A survey. Computers in Industry, 66, 1–10. https://doi.org/10.1016/j.compind.2014.10.006
Hung, C.-W., Jiang, J.-G., P. Wu, H.-H., & Mao, W.-L. (2018). An Automated Optical Inspection system for a tube inner circumference state identification. Proceedings of International Conference on Artificial Life and Robotics, 23(4), 415–418. https://doi.org/10.5954/icarob.2018.os8-1
Issam, B. K., & Mohamed, L. (2008). Support vector regression based residual MCUSUM control chart for autocorrelated process. Applied Mathematics and Computation, 201(1–2), 565–574. https://doi.org/10.1016/j.amc.2007.12.059
Jarrett, J. E., & Pan, X. (2007). The quality control chart for monitoring multivariate autocorrelated processes. Computational Statistics and Data Analysis, 51(8), 3862–3870. https://doi.org/10.1016/j.csda.2006.01.020
Kang, J. H., Yu, J., & Kim, S. B. (2016). Adaptive nonparametric control chart for time-varying and multimodal processes. Journal of Process Control, 37, 34–45. https://doi.org/10.1016/j.jprocont.2015.11.005
Khediri, I. Ben, Weihs, C., & Limam, M. (2010). Support Vector Regression control charts for multivariate nonlinear autocorrelated processes. Chemometrics and Intelligent Laboratory Systems, 103(1), 76–81. https://doi.org/10.1016/j.chemolab.2010.05.021
Leng, J., Wang, D., Shen, W., Li, X., Liu, Q., & Chen, X. (2021). Digital twins-based smart manufacturing system design in Industry 4.0: A review. Journal of Manufacturing Systems, 60(May), 119–137. https://doi.org/10.1016/j.jmsy.2021.05.011
Leoni, R. C., Costa, A. F. B., & Machado, M. A. G. (2015). The effect of the autocorrelation on the performance of the T2 chart. European Journal of Operational Research, 247(1), 155–165. https://doi.org/10.1016/j.ejor.2015.05.077
Li, C., Mukherjee, A., Su, Q., & Xie, M. (2016). Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location. International Journal of Production Research, 54(24), 7259–7273. https://doi.org/10.1080/00207543.2016.1173254
Li, J., Jeske, D. R., Zhou, Y., & Zhang, X. (2019). A wavelet-based nonparametric CUSUM control chart for autocorrelated processes with applications to network surveillance. In Quality and Reliability Engineering International (Vol. 35, Issue 2, pp. 644–658). https://doi.org/10.1002/qre.2427
Li, Y., Pan, E., & Xiao, Y. (2020). On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes. Quality and Reliability Engineering International, 36(7), 2351–2369. https://doi.org/10.1002/qre.2701
Liang, W., Pu, X., & Xiang, D. (2017). A distribution-free multivariate CUSUM control chart using dynamic control limits. Journal of Applied Statistics, 44(11), 2075–2093. https://doi.org/10.1080/02664763.2016.1247784
Liu, H., Yu, Y., Sun, F., & Gu, J. (2017). Visual – Tactile Fusion for Object Recognition. IEEE Transactions on Automation Science and Engineering, 14(2), 996–1008.
Moraes, D. A. O., Oliveira, F. L. P., Duczmal, L. H., & Cruz, F. R. B. (2016). Comparing the inertial effect of MEWMA and multivariate sliding window schemes with confidence control charts. International Journal of Advanced Manufacturing Technology, 84(5–8), 1457–1470. https://doi.org/10.1007/s00170-015-7822-7
Mowery, D. C. (2010). The influence of market demand upon innovation: a critical review of some recent empirical studies. Inside the Black Box, 8, 193–242. https://doi.org/10.1017/cbo9780511611940.011
Nguyen, H. Du, Nadi, A. A., Tran, K. D., Castagliola, P., Celano, G., & Tran, K. P. (2023). The Shewhart-type RZ control chart for monitoring the ratio of autocorrelated variables. International Journal of Production Research, 61(20), 6746–6771. https://doi.org/10.1080/00207543.2022.2137594
Nujoom, R., Mohammed, A., & Wang, Q. (2018). A sustainable manufacturing system design: A fuzzy multi-objective optimization model. Environmental Science and Pollution Research, 25(25), 24535–24547. https://doi.org/10.1007/s11356-017-9787-6
Ojer, M., Serrano, I., Saiz, F., Barandiaran, I., Gil, I., Aguinaga, D., & Alejandro, D. (2020). Real-time automatic optical system to assist operators in the assembling of electronic components. International Journal of Advanced Manufacturing Technology, 107(5–6), 2261–2275. https://doi.org/10.1007/s00170-020-05125-z
Park, J., & Jun, C. H. (2015). A new multivariate EWMA control chart via multiple testing. Journal of Process Control, 26, 51–55. https://doi.org/10.1016/j.jprocont.2015.01.007
Prieto, F., Redarce, T., Lepage, R., & Boulanger, P. (2002). An Automated Inspection System. 917–925.
Psarakis, S. (2015). Adaptive Control Charts: Recent Developments and Extensions. Quality and Reliability Engineering International, 31(7), 1265–1280. https://doi.org/10.1002/qre.1850
Quinino, R. C., Cruz, F. R. B., & Quinino, V. B. (2021). Control chart for process mean monitoring combining variable and attribute inspections. Computers and Industrial Engineering, 152(October 2020), 106996. https://doi.org/10.1016/j.cie.2020.106996
Quintero-Arteaga, C., Peñabaena-Niebles, R., Vélez, J. I., & Jubiz-Diaz, M. (2022). Statistical design of an adaptive synthetic X¯$ar{X}$ control chart for autocorrelated processes. Quality and Reliability Engineering International, 38(5), 2475–2500. https://doi.org/10.1002/qre.3086
Psarakis S. & G. E. A. Papaleonida. (2007). SPC Procedures for Monitoring Autocorrelated. Quality Technology & Quantitative Management, 4(4), 501–540. https://doi.org/10.1080/16843703.2007.11673168
Reynolds, M. R., & Lu, C. W. (1997). Control charts for monitoring processes with autocorrelated data. Nonlinear Analysis, Theory, Methods and Applications, 30(7), 4059–4067. https://doi.org/10.1016/S0362-546X(97)00011-4
Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 1(3), 239–250. https://doi.org/10.1080/00401706.1959.10489860
Sabahno, H., Castagliola, P., & Amiri, A. (2020). An adaptive variable-parameters scheme for the simultaneous monitoring of the mean and variability of an autocorrelated multivariate normal process. Journal of Statistical Computation and Simulation, 90(8), 1430–1465. https://doi.org/10.1080/00949655.2020.1730373
Sabahno, H., & Celano, G. (2023). Monitoring the multivariate coefficient of variation in presence of autocorrelation with variable parameters control charts. Quality Technology and Quantitative Management, 20(2), 184–210. https://doi.org/10.1080/16843703.2022.2075193
Sampaio, E. S., Ho, L. L., & De Medeirosc, P. G. (2014). A combined npx X¯ control chart to monitor the process mean in a two-stage sampling. Quality and Reliability Engineering International, 30(7), 1003–1013. https://doi.org/10.1002/qre.1528
Schmookler, J. (2016). Changes in Industry and in the State of Knowledge as Determinants of Industrial Invention. In The Rate and Direction of Inventive Activity. https://doi.org/10.1515/9781400879762-007
Simões, F. D., Leoni, R. C., MacHado, M. A. G., & Costa, A. F. B. (2016). Synthetic charts to control bivariate processes with autocorrelated data. Computers and Industrial Engineering, 97, 15–25. https://doi.org/10.1016/j.cie.2016.04.005
Steiner, S. H., & Jock MacKay, R. (2004). Effective Monitoring of Processes with Parts Per Million Defective. A Hard Problem! Frontiers in Statistical Quality Control 7, 140–149. https://doi.org/10.1007/978-3-7908-2674-6_10
Sun, J., Zhou, S., & Veeramani, D. (2023). A neural network-based control chart for monitoring and interpreting autocorrelated multivariate processes using layer-wise relevance propagation. Quality Engineering, 35(1), 33–47. https://doi.org/10.1080/08982112.2022.2087041
Travaglioni, M., Piscitelli, G., & Petrillo, A. (2020). Smart-manufacturing-systems-and-applied-industrial-technologies-for-a-sustainable-industry-A-systematic-literature-review2020Applied-Sciences-Switzerland.pdf.
Vanhatalo, E., & Kulahci, M. (2015). The Effect of Autocorrelation on the Hotelling T2 Control Chart. Quality and Reliability Engineering International, 31(8), 1779–1796. https://doi.org/10.1002/qre.1717
Wang, J., Li, Y., Gao, R. X., & Zhang, F. (2022). Hybrid physics-based and data-driven models for smart manufacturing: Modelling, simulation, and explainability. Journal of Manufacturing Systems, 63(April), 381–391. https://doi.org/10.1016/j.jmsy.2022.04.004
Wang, K. J., & Asrini, L. J. (2022). Deep learning-based automatic optical inspection system empowered by online multivariate autocorrelated process control. International Journal of Advanced Manufacturing Technology, 120(9–10), 6143–6162. https://doi.org/10.1007/s00170-022-09161-9
Wang, K. J., & Asrini, L. J. (2023). Multivariate auto-correlated process control by a residual-based mixed CUSUM-EWMA model. Quality and Reliability Engineering International, 39(4), 1120–1142. https://doi.org/10.1002/qre.3278
Xie, M., & Goh, T. N. (1993). Improvement Detection by Control Charts for High Yield Processes. International Journal of Quality & Reliability Management, 10(7). https://doi.org/10.1108/02656719310043779
Xu, S., An, X., Qiao, X., Zhu, L., & Li, L. (2013). Multi-output least-squares support vector regression machines. Pattern Recognition Letters, 34(9), 1078–1084. https://doi.org/10.1016/j.patrec.2013.01.015
Yao, Y., Chakraborti, S., Yang, X., Parton, J., Lewis, D., & Hudnall, M. (2023). Phase I control chart for individual autocorrelated data: application to prescription opioid monitoring. Journal of Quality Technology, 55(3), 302–317. https://doi.org/10.1080/00224065.2022.2139783
Zaman, B., Abbas, N., Riaz, M., & Lee, M. H. (2016). Mixed CUSUM-EWMA chart for monitoring process dispersion. International Journal of Advanced Manufacturing Technology, 86(9–12), 3025–3039. https://doi.org/10.1007/s00170-016-8411-0
Zaman, B., Lee, M. H., Riaz, M., & Abujiya, M. R. (2020a). An improved process monitoring by mixed multivariate memory control charts: An application in wind turbine field. Computers and Industrial Engineering, 142(January), 106343. https://doi.org/10.1016/j.cie.2020.106343
Zaman, B., Lee, M. H., Riaz, M., & Abujiya, M. R. (2020b). An improved process monitoring by mixed multivariate memory control charts: An application in wind turbine field. Computers and Industrial Engineering, 142(September 2019), 106343. https://doi.org/10.1016/j.cie.2020.106343
Zhou, Q., Zou, C., Wang, Z., & Jiang, W. (2012). Likelihood-based EWMA charts for monitoring poisson count data with time-varying sample sizes. Journal of the American Statistical Association, 107(499), 1049–1062. https://doi.org/10.1080/01621459.2012.682811
Zhou, W., Cheng, C., & Zheng, Z. (2019). Optimal design of an attribute control chart for monitoring the mean of autocorrelated processes. Computers and Industrial Engineering, 137(January). https://doi.org/10.1016/j.cie.2019.106081
Zou, C., & Tsung, F. (2010). Likelihood ratio-based distribution-free EWMA control charts. Journal of Quality Technology, 42(2), 174–196. https://doi.org/10.1080/00224065.2010.11917815