An efficient adaptive r-MD multivariate single control chart for nonlinear multiple quality characteristics

References

• Adegoke, N. A., J. O. Ajadi, A. Mukherjee, and S. A. Abbasi. 2022. “Nonparametric Multivariate Covariance Chart for Monitoring Individual Observations.” Computers & Industrial Engineering 167: 108025. doi:10.1016/j.cie.2022.108025
   Web of Science ®Google Scholar
• Ajadi, Jimoh Olawale, Zezhong Wang, and Inez Maria Zwetsloot. 2021. “A Review of Dispersion Control Charts for Multivariate Individual Observations.” Quality Engineering 33 (1): 60–75. doi:10.1080/08982112.2020.1755438
   Web of Science ®Google Scholar
• Ajadi, J. O., A. Wong, T. Mahmood, and K. Hung. 2022. “A new Multivariate CUSUM Chart for Monitoring of Covariance Matrix with Individual Observations Under Estimated Parameter.” Quality and Reliability Engineering International 38 (2): 834–847. doi:10.1002/qre.3017
   Web of Science ®Google Scholar
• Apsemidis, A., S. Psarakis, and J. M. Moguerza. 2020. “A Review of Machine Learning Kernel Methods in Statistical Process Monitoring.” Computers & Industrial Engineering 142: 106376. doi:10.1016/j.cie.2020.106376
   Web of Science ®Google Scholar
• Bartels, Robert. 1982. “The Rank Version of von Neumann’s Ratio Test for Randomness.” Journal of the American Statistical Association 77 (377): 40–46. doi:10.1080/01621459.1982.10477764
   Web of Science ®Google Scholar
• Boone, J. M., and S. Chakraborti. 2012. “Two Simple Shewhart-Type Multivariate Nonparametric Control Charts.” Applied Stochastic Models in Business and Industry 28 (2): 130–140. doi:10.1002/asmb.900
   Web of Science ®Google Scholar
• Chakraborti, S., and M. A. Graham. 2019. “Nonparametric (Distribution-Free) Control Charts: An Updated Overview and Some Results.” Quality Engineering 31 (4): 523–544. doi:10.1080/08982112.2018.1549330.
   Web of Science ®Google Scholar
• Crosier, Ronald B. 1988. “Multivariate Generalisations of Cumulative Sum Quality-Control Schemes.” Technometrics 30 (3): 291–303. doi:10.1080/00401706.1988.10488402
   Web of Science ®Google Scholar
• Ebadi, M., S. Chenouri, D. K. Lin, and H. Steiner. 2022. “Statistical Monitoring of the Covariance Matrix in Multivariate Processes: A Literature Review.” Journal of Quality Technology 54 (3): 269–289. doi:10.1080/00224065.2021.1889419
   Web of Science ®Google Scholar
• Faraz, A., E. Saniga, and D. Montgomery. 2019. “Percentile-Based Control Chart Design with an Application to Shewhart X¯ and S2 Control Charts.” Quality and Reliability Engineering International 35 (1): 116–126. doi:10.1002/qre.2384
   Web of Science ®Google Scholar
• Gomes, J. H. F., A. P. Paiva, S. C. Costa, P. P. Balestrassi, and E. J. Paiva. 2013. “Weighted Multivariate Mean Square Error for Processes Optimisation: A Case Study on Flux-Cored arc Welding for Stainless Steel Claddings.” European Journal of Operational Research 226 (3): 522–535. doi:10.1016/j.ejor.2012.11.042
   Web of Science ®Google Scholar
• Graham, M. A., S. Chakraborti, and A. Mukherjee. 2014. “Design and Implementation of CUSUM Exceedance Control Charts for Unknown Location.” International Journal of Production Research 52 (18): 5546–5564. doi:10.1080/00207543.2014.917214
   Web of Science ®Google Scholar
• Hajlaoui, Mekki. 2010. “A Graphical Quality Control Procedure Using Data Depth.” Advances and Applications in Statistics 19 (2): 97–111.
   Google Scholar
• Hajlaoui, Mekki. 2011. “On the Charting Procedures: T 2 Chart and DD-Diagram.” International Journal of Quality, Statistics, and Reliability 2011. doi:10.1155/2011/830764.
   Google Scholar
• Hastie, Trevor, Robert Tibshirani, Gareth James, and Daniela Witten. 2021. An Introduction to Statistical Learning: with Applications in R. 2nd ed. New York: Springer.
   Google Scholar
• Hawkins, D. M., and Q. Deng. 2009. “Combined Charts for Mean and Variance Information.” Journal of Quality Technology 41 (4): 415–425. doi:10.1080/00224065.2009.11917795
   Web of Science ®Google Scholar
• He, Shuguang, Wei Jiang, and Houtao Deng. 2018. “A Distance-Based Control Chart for Monitoring Multivariate Processes Using Support Vector Machines.” Annals of Operations Research 263 (1–2): 191–207. doi:10.1007/s10479-016-2186-4.
   Web of Science ®Google Scholar
• Henze, N., and B. Zirkler. 1990. “A Class of Invariant Consistent Tests for Multivariate Normality.” Communications in Statistics – Theory and Methods 19 (10): 3595–3617. doi:10.1080/03610929008830400
   Web of Science ®Google Scholar
• Hotelling, H. 1947. “Multivariate Quality Control-Illustrated by the air Testing of Sample Bombsights.” Techniques of Statistical Analysis, 111–184.
   Google Scholar
• Huwang, Longcheen, Li Wei Lin, and Cheng Ting Yu. 2019. “A Spatial Rank–Based Multivariate EWMA Chart for Monitoring Process Shape Matrices.” Quality and Reliability Engineering International 35 (6): 1716–1734. doi:10.1002/qre.2471
   Web of Science ®Google Scholar
• Huwang, Longcheen, Arthur B. Yeh, and Chien Wei Wu. 2007. “Monitoring Multivariate Process Variability for Individual Observations.” Journal of Quality Technology 39 (3): 258–278. doi:10.1080/00224065.2007.11917692
   Web of Science ®Google Scholar
• Khoo, Michael B.C., V. H. Wong, Zhang Wu, and Philippe Castagliola. 2012. “Optimal Design of the Synthetic Chart for the Process Mean Based on Median Run Length.” IIE Transactions (Institute of Industrial Engineers) 44 (9): 765–779. doi:10.1080/0740817X.2011.609526.
   Web of Science ®Google Scholar
• Kim, J., M. K. Jeong, E. A. Elsayed, K. N. Al-Khalifa, and A. M. S. Hamouda. 2016. “An Adaptive Step-Down Procedure for Fault Variable Identification.” International Journal of Production Research 54 (11): 3187–3200. doi:10.1080/00207543.2015.1076948
   Web of Science ®Google Scholar
• Lee, Seulki, Mingu Kwak, Kwok Leung Tsui, and Seoung Bum Kim. 2019. “Process Monitoring Using Variational Autoencoder for High-Dimensional Nonlinear Processes.” Engineering Applications of Artificial Intelligence 83 (August 2018): 13–27. doi:10.1016/j.engappai.2019.04.013.
   Google Scholar
• Li, Wendong, Chi Zhang, Fugee Tsung, and Yajun Mei. 2021. “Nonparametric Monitoring of Multivariate Data via KNN Learning.” International Journal of Production Research 59 (20): 6311–6326. doi:10.1080/00207543.2020.1812750.
   Web of Science ®Google Scholar
• Li, Zhonghua, Changliang Zou, Zhaojun Wang, and Longcheen Huwang. 2013. “A Multivariate Sign Chart for Monitoring Process Shape Parameters.” Journal of Quality Technology 45 (2): 149–165. doi:10.1080/00224065.2013.11917923
   Web of Science ®Google Scholar
• Liu, Regina Y. 1995. “Control Charts for Multivariate Processes.” Journal of the American Statistical Association 90 (432): 1380–1387. doi:10.1080/01621459.1995.10476643
   Web of Science ®Google Scholar
• Liu, Regina Y., and Kesar Singh. 1993. “A Quality Index Based on Data Depth and Multivariate Rank Tests.” Journal of the American Statistical Association 88 (421): 252–260. doi:10.2307/2290720.
   Web of Science ®Google Scholar
• Liu, Regina Y., Kesar Singh, and Julie H. Teng*. 2004. “DDMA-Charts: Nonparametric Multivariate Moving Average Control Charts Based on Data Depth.” Allgemeines Statistisches Archiv 88 (2): 235–258. doi:10.1007/s101820400170
   Google Scholar
• Lowry, Cynthia A., and Douglas C. Montgomery. 1995. “A Review of Multivariate Control Charts.” IIE Transactions (Institute of Industrial Engineers) 27 (6): 800–810. doi:10.1080/07408179508936797.
   Web of Science ®Google Scholar
• Maboudou-Tchao, Edgard M., and Douglas M. Hawkins. 2011. “Self-Starting Multivariate Control Charts for Location and Scale.” Journal of Quality Technology 43 (2): 113–126. doi:10.1080/00224065.2011.11917850
   Web of Science ®Google Scholar
• Maji, Arijit, and Indrajit Mukherjee. 2021. “An Unsupervised One-Class-Classifier Support Vector Machine to Simultaneously Monitor Location and Scale of Multivariate Quality Characteristics.” International Journal of Quality & Reliability Management. Advance Online Publication, doi:10.1108/IJQRM-09-2021-0316.
   Google Scholar
• Mccracken, A. K., and S. Chakraborti. 2013. “Control Charts for Joint Monitoring of Mean and Variance: An Overview.” Quality Technology and Quantitative Management 10 (1): 17–36. doi:10.1080/16843703.2013.11673306
   Web of Science ®Google Scholar
• Mitra, A., K. B. Lee, and S. Chakraborti. 2019. “An Adaptive Exponentially Weighted Moving Average-Type Control Chart to Monitor the Process Mean.” European Journal of Operational Research 279 (3): 902–911. doi:10.1016/j.ejor.2019.07.002
   Web of Science ®Google Scholar
• Montgomery, Douglas C. 2009. Introduction to Statistical Quality Control. 5th ed. New York: John Willey & Sons.
   Google Scholar
• Mukherjee, Amitava, and Marco Marozzi. 2020. “Nonparametric Phase-II Control Charts for Monitoring High-Dimensional Processes with Unknown Parameters.” Journal of Quality Technology. Advance online Publication. doi:10.1080/00224065.2020.1805378.
   Web of Science ®Google Scholar
• Qiu, Peihua. 2018. “Some Perspectives on Nonparametric Statistical Process Control.” Journal of Quality Technology 50 (1): 49–65. doi:10.1080/00224065.2018.1404315
   Web of Science ®Google Scholar
• Ranjan, Chitta, and Vahab Najari. 2020. “nlcor: Compute Nonlinear Correlations.” In:Research Gate (2020). doi:10.13140/RG.2.2.33716.68480.
   Google Scholar
• Silver, E. A., and T. R. Rohleder. 1999. “The Economic Design of an X Control Chart Recognizing Process Improvement.” International Journal of Production Research 37 (2): 393–412. doi:10.1080/002075499191832.
   Web of Science ®Google Scholar
• Sukchotrat, Thuntee, Seoung Bum Kim, and Fugee Tsung. 2010. “One-Class Classification-Based Control Charts for Multivariate Process Monitoring.” IIE Transactions (Institute of Industrial Engineers) 42 (2): 107–120. doi:10.1080/07408170903019150.
   Google Scholar
• Sun, Ruixiang, and Fugee Tsung. 2003. “A Kernel-Distance-Based Multivariate Control Chart Using Support Vector Methods.” International Journal of Production Research 41 (13): 2975–2989. doi:10.1080/1352816031000075224
   Web of Science ®Google Scholar
• Székely, Gábor J., and Maria L. Rizzo. 2009. “Brownian Distance Covariance.” Annals of Applied Statistics 3 (4): 1236–1265. doi:10.1214/09-AOAS312.
   Web of Science ®Google Scholar
• Turkoz, M., S. Kim, Y. S. Jeong, M. K. Jeong, E. A. Elsayed, K. N. Al-Khalifa, and A. M. Hamouda. 2019. “Bayesian Framework for Fault Variable Identification.” Journal of Quality Technology 51 (4): 375–391. doi:10.1080/00224065.2018.1507561
   Web of Science ®Google Scholar
• Verdier, Ghislain, and Ariane Ferreira. 2011. “Adaptive Mahalanobis Distance and K-Nearest Neighbor Rule for Fault Detection in Semiconductor Manufacturing.” IEEE Transactions on Semiconductor Manufacturing 24 (1): 59–68. doi:10.1109/TSM.2010.2065531
   Web of Science ®Google Scholar
• Vining, Geoff. 2009. “Technical Advice: Phase I and Phase II Control Charts.” Quality Engineering 21 (4): 478–479. doi:10.1080/08982110903185736
   Web of Science ®Google Scholar
• Wheeler, R. E. 2004. “Comments on algorithmic design”. Vignette accompanying package AlgDe.
   Google Scholar
• Yang, S., J. Wang, Y. Tu, Y. Han, X. Ren, C. Ding, and X. Chen. 2022. “Robust Multi-Response Surface Optimisation Based on Bayesian Quantile Model.” International Journal of Production Research, 1–19. doi:10.1080/00207543.2022.2079014.
   Web of Science ®Google Scholar
• Yeh, Arthur B., Longcheen Huwang, and W. U. Chien-Wei. 2005. “A Multivariate EWMA Control Chart for Monitoring Process Variability with Individual Observations.” IIE Transactions (Institute of Industrial Engineers) 37 (11): 1023–1035. doi:10.1080/00224065.2007.11917692.
   Web of Science ®Google Scholar
• Zhang, G., and S. I. Chang. 2008. “Multivariate EWMA Control Charts Using Individual Observations for Process Mean and Variance Monitoring and Diagnosis.” International Journal of Production Research 46 (24): 6855–6881. doi:10.1080/00207540701197028
   Web of Science ®Google Scholar
• Zhang, Jiujun, Zhonghua Li, and Zhaojun Wang. 2010. “A Multivariate Control Chart for Simultaneously Monitoring Process Mean and Variability.” Computational Statistics and Data Analysis 54 (10): 2244–2252. doi:10.1016/j.csda.2010.03.027
   Web of Science ®Google Scholar
• Zou, Changliang, and Fugee Tsung. 2011. “A Multivariate Sign EWMA Control Chart.” Technometrics 53 (1): 84–97. doi:10.1198/TECH.2010.09095
   Web of Science ®Google Scholar