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Article

Copula-based multivariate EWMA control charts for monitoring the mean vector of bivariate processes using a mixture model

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Pages 4211-4234 | Received 21 Feb 2022, Accepted 30 Jan 2023, Published online: 23 Feb 2023

References

  • Alqawba, M., J. M. Kim, and T. Radwan. 2022. Residual-based cumulative sum charts to monitor time series of counts via copula-based Markov models. Applied Stochastic Models in Business and Industry 38 (6):1039–1048. doi: 10.1002/asmb.2703.
  • Benoumechiara, N., N. Bousquet, B. Michel, and P. Saint-Pierre. 2020. Detecting and modeling critical dependence structures between random inputs of computer models. Dependence Modeling 8 (1):263–97. doi: 10.1515/demo-2020-0016.
  • Castagliola, P., G. Celano, D. Rahali, and S. Wu. 2022. Control charts for monitoring time-between-events-and-amplitude data. In Control charts and machine learning for anomaly detection in manufacturing, pp. 43–76. Cham: Springer. doi: 10.1007/978-3-030-83819-5-3
  • Celano, G., P. Castagliola, E. Trovato, and S. Fichera. 2011. Shewhart and EWMA t control charts for short production runs. Quality and Reliability Engineering International 27 (3):313–26. doi: 10.1002/qre.1121.
  • Chollete, L., V. de la Pena, and C. C. Lu. 2011. International diversification: A copula approach. Journal of Banking & Finance 35 (2):403–17. doi: 10.1016/j.jbankfin.2010.08.020.
  • Chong, N. L., M. B. Khoo, A. Haq, and P. Castagliola. 2019. Hotelling’s T2 control charts with fixed and variable sample sizes for monitoring short production runs. Quality and Reliability Engineering International 35 (1):14–29. doi: 10.1002/qre.2377.
  • Crosier, R. B. 1988. Multivariate generalizations of cumulative sum quality-control schemes. Technometrics 30 (3):291–303. doi: 10.1177/0008068320130109.
  • Dokouhaki, P., and R. Noorossana. 2013. A Copula Markov CUSUM chart for monitoring the bivariate auto-correlated binary observations. Quality and Reliability Engineering International 29 (6):911–9. doi: 10.1002/qre.1450.
  • Easton, A., O. van Dalen, R. Goeb, and A. Di Bucchianico. 2022. Bivariate copula monitoring. Quality and Reliability Engineering International 38 (3):1272–88. doi: 10.1002/qre.3034.
  • Fatahi, A. A., P. Dokouhaki, and B. F. Moghaddam. 2011. A bivariate control chart based on copula function. In 2011 IEEE International Conference on Quality and Reliability, pp. 292–6. IEEE, September. doi: 10.1109/ICQR.2011.6031728.
  • Fatahi, A. A., R. Noorossana, P. Dokouhaki, and B. F. Moghaddam. 2012. Copula-based bivariate ZIP control chart for monitoring rare events. Communications in Statistics-Theory and Methods 41 (15):2699–716. doi: 10.1080/03610926.2011.556296.
  • Fermanian, J. D., and O. Scaillet. 2004. Some statistical pitfalls in copula modeling for financial applications. FAME Research Paper Series rp108. International Center for Financial Asset Management and Engineering. doi: 10.2139/ssrn.558981.
  • Flores, Y. S., and A. Díaz-Hernández. 2021. The general tail dependence function in the marshall-olkin and other parametric copula models with an application to financial time series. Sankhya B 84, 1–42. doi: 10.1007/s13571-020-00241-y.
  • Geenens, G. 2020. Copula modeling for discrete random vectors. Dependence Modeling 8 (1):417–40. doi: 10.1515/demo-2020-0022.
  • Hotteling, H. 1947. Multivariate quality control, illustrated by the air testing of sample bombsights. Techniques of Statistical Analysis 111–84.
  • Hryniewicz, O. 2012. On the robustness of the Shewhart control chart to different types of dependencies in data. In Frontiers in statistical quality control 10, pp. 19–33. Heidelberg: Physica. doi: 10.1007/978-3-7908-2846-7-2.
  • Hu, L. 2006. Dependence patterns across financial markets: a mixed copula approach. Applied Financial Economics 16 (10):717–29. doi: 10.1080/09603100500426515.
  • Kim, J. M., J. Baik, and M. Reller. 2021. Control charts of mean and variance using copula Markov SPC and conditional distribution by copula. Communications in Statistics-Simulation and Computation 50 (1):85–102. doi: 10.1080/03610918.2018.1547404.
  • Li, Y., and X. Pu. 2012. On the performance of two-sided control charts for short production runs. Quality and Reliability Engineering International 28 (2):215–32. doi: 10.1002/qre.1237.
  • Liu, Y. P., J. H. Liu, and P. Shao. 2013. Pricing basket credit default swap based on mix copula functions. In The 19th International Conference on Industrial Engineering and Engineering Management, pp. 805–13. Springer, Berlin, Heidelberg. doi: 10.1007/978-3-642-38433-2.
  • Lowry, C. A., W. H. Woodall, C. W. Champ, and S. E. Rigdon. 1992. A multivariate exponentially weighted moving average control chart. Technometrics 34 (1):46–53. doi: 10.1080/00401706.1992.10485232.
  • Mason, R. L., and J. C. Young. 2002. Multivariate statistical process control with industrial applications. Philadelphia, Pennsylvania: Society for Industrial and Applied Mathematics. doi: 10.1137/1.9780898718461.fm.
  • Moharib Alsarray, R. M., J. Kazempoor, and A. Ahmadi Nadi. 2021. Monitoring the Weibull shape parameter under progressive censoring in presence of independent competing risks. Journal of Applied Statistics 1–18. doi: 10.1080/02664763.2021.2003760.
  • Montgomery, D. C. 2020. Introduction to statistical quality control. New York: John Wiley & Sons.
  • Nelsen, R. B. 2007. An introduction to copulas. New York: Springer Science & Business Media. doi: 10.1007/0-387-28678-0.
  • Pascual, F. G., and S. B. Akhundjanov. 2020. Copula-based control charts for monitoring multivariate Poisson processes with application to hepatitis C counts. Journal of Quality Technology 52 (2):128–44. doi: 10.1080/00224065.2019.1571337.
  • Prabhu, S. S., and G. C. Runger. 1997. Designing a multivariate EWMA control chart. Journal of Quality Technology 29 (1):8–15. doi: 10.1080/00224065.1997.11979720.
  • Qian, D., B. Wang, X. Qing, T. Zhang, Y. Zhang, X. Wang, and M. Nakamura. 2016. Drowsiness detection by Bayesian-copula discriminant classifier based on EEG signals during daytime short nap. IEEE Transactions on Biomedical Engineering 64 (4):743–54. doi: 10.1109/TBME.2016.2574812.
  • Sasiwannapong, S., S. Sukparungsee, P. Busababodhin, and Y. Areepong, 2022. The efficiency of constructed bivariate copulas for MEWMA and Hotelling’s T2 control charts. Communications in Statistics-Simulation and Computation 51 (4):1837–51. doi: 10.1080/03610918.2019.1687719.
  • Singla, N., K. Jain, and S. K. Sharma. 2016. Goodness of fit tests and power comparisons for weighted gamma distribution. REVSTAT-Statistical Journal 14 (1):29–48.
  • Sklar, A. 1973. Random variables, joint distribution functions, and copulas. Kybernetika 9 (6):449–60.
  • Stoumbos, Z. G., and J. H. Sullivan. 2002. Robustness to non-normality of the multivariate EWMA control chart. Journal of Quality Technology 34 (3):260–76. doi: 10.1080/00224065.2002.11980157.
  • Sukparungsee, S., S. Kuvattana, P. Busababodhin, and Y. Areepong. 2018. Bivariate copulas on the Hotelling’s T 2 control chart. Communications in Statistics-Simulation and Computation 47 (2):413–9. doi: 10.1080/03610918.2016.1228958.
  • Sukparungsee, S., S. Sasiwannapong, P. Busababodhin, and Y. Areepong. 2021. The effects of constructed bivariate copulas on multivariate control charts effectiveness. Quality and Reliability Engineering International 37 (5):2156–68. doi: 10.1002/qre.2850.
  • Tiengket, S., S. Sukparungsee, P. Busababodhin, and Y. Areepong. 2020. Construction of bivariate copulas on the Hotelling’s T2 control chart. Thailand Statistician 18 (1):1–15.
  • Tran, K. D., A. A. Nadi, T. H. Nguyen, and K. P. Tran. 2021. One-sided Shewhart control charts for monitoring the ratio of two normal variables in short production runs. Journal of Manufacturing Processes 69:273–89. doi: 10.1016/j.jmapro.2021.07.031.
  • Wang, F. K. 2006. Quality evaluation of a manufactured product with multiple characteristics. Quality and Reliability Engineering International 22 (2):225–36. doi: 10.1002/qre.712.
  • Wu, C., S. Si, W. Huang, and W. Jiang. 2022. Copula-based CUSUM charts for monitoring infectious disease using Markovian Poisson processes. Computers and Industrial Engineering 108536. doi: 10.1016/j.cie.2022.108536.
  • Wu, C., and S. Si. 2022. Bivariate copula-based CUSUM charts for monitoring conditional nonlinear processes with first-order autocorrelation. Journal of Statistical Computation and Simulation 92 (16):3373–3399. doi: 10.1080/00949655.2022.2066104.
  • Zheng, C., M. Egan, L. Clavier, G. W. Peters, and J. M. Gorce. 2019, Copula-based interference models for IoT wireless networks. In ICC 2019-2019 IEEE International Conference on Communications (ICC), pp. 1–6. IEEE, May. doi: 10.1109/ICC.2019.8761783.

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