EWMA Robust Max-M Control Chart for Synthetic and Real Data

Samin Radjid; Wibawati Wibawati; Muhammad Ahsan

doi:10.30598/parameterv5i1pp219-232

Samin Radjid Institut Teknologi Sepuluh Nopember
Wibawati Wibawati Institut Teknologi Sepuluh Nopember, Indonesia
Muhammad Ahsan

DOI: https://doi.org/10.30598/parameterv5i1pp219-232

Keywords: clinker, ERMM-Chart, EWMA, Fast-MCD, simultaneous control chart

Abstract

Quality monitoring in multivariate industrial processes requires a control chart that can simultaneously evaluate changes in the process mean and variability. This study applies the Exponentially Weighted Moving Average Robust Max-M Control Chart (ERMM-Chart) to synthetic data and real cement clinker quality data. The ERMM-Chart is constructed from a robust Max-M statistic that monitors the mean and variability components, followed by an Exponentially Weighted Moving Average (EWMA) smoothing mechanism. Phase I parameters are estimated using the Fast Minimum Covariance Determinant (Fast-MCD) method to obtain robust estimates of the process center and covariance matrix. The synthetic data are used to illustrate the response of the ERMM-Chart under no-shift, mean-shift, variability-shift, and simultaneous mean-variability shift conditions. Meanwhile, the real clinker data are analyzed using two quality characteristics, namely free lime (FCaO) and tetracalcium aluminoferrite (C₄AF). The results show that the ERMM-Chart can distinguish the reference phase from the monitoring phase through statistic points exceeding the upper control limit. The chart also provides early detection of process changes based on the Run Length value. Thus, the ERMM-Chart can be used as a robust simultaneous multivariate control chart for individual observations.

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References

[1] D. C. Montgomery, Introduction to Statistical Quality Control, 8th ed. Hoboken, NJ, USA: John Wiley & Sons, 2020.
[2] C. A. Lowry, W. H. Woodall, C. W. Champ, and S. E. Rigdon, “A multivariate exponentially weighted moving average control chart,” Technometrics, vol. 34, no. 1, pp. 46–53, 1992, doi: 10.1080/00401706.1992.10485232.
[3] H. Hotelling, “Multivariate quality control, illustrated by the air testing of sample bombsights,” in Techniques of Statistical Analysis, C. Eisenhart, M. W. Hastay, and W. A. Wallis, Eds. New York, NY, USA: McGraw-Hill, 1947, pp. 113–184.
[4] M. B. C. Khoo and S. H. Quah, “Multivariate control chart for process dispersion based on individual observations,” Quality Engineering, vol. 15, no. 4, pp. 639–642, 2003, doi: 10.1081/QEN-120018394.
[5] M. A. Djauhari, “Improved monitoring of multivariate process variability,” Journal of Quality Technology, vol. 37, no. 1, pp. 32–39, 2005, doi: 10.1080/00224065.2005.11980298.
[6] M. A. Djauhari, M. Mashuri, and D. E. Herwindiati, “Multivariate process variability monitoring,” Communications in Statistics - Theory and Methods, vol. 37, no. 11, pp. 1742–1754, 2008, doi: 10.1080/03610920701826286.
[6] R. Kruba, M. Mashuri, and D. D. Prastyo, “The effectiveness of Max-Half-Mchart over Max-Mchart in simultaneously monitoring process mean and variability of individual observations,” Quality and Reliability Engineering International, vol. 37, no. 6, pp. 2334–2347, 2021, doi: 10.1002/qre.2860.
[7] M. B. C. Khoo, “A new bivariate control chart to monitor the multivariate process mean and variance simultaneously,” Quality Engineering, vol. 17, no. 1, pp. 109–118, 2004, doi: 10.1081/QEN-200028718.
[8] G. Chen and S. W. Cheng, “MAX chart: Combining X-bar chart and S chart,” Statistica Sinica, vol. 8, pp. 263–271, 1998.
[9] K. Thaga and L. Gabaitiri, “Multivariate Max-Chart,” Economic Quality Control, vol. 21, no. 1, pp. 113–125, 2006, doi: 10.1515/EQC.2006.113.
[10] R. Kruba, M. Mashuri, and D. D. Prastyo, “The effectiveness of Max-Half-Mchart over Max-Mchart in simultaneously monitoring process mean and variability of individual observations,” Quality and Reliability Engineering International, vol. 37, no. 6, pp. 2334–2347, 2021, doi: 10.1002/qre.2860.
[11] S. W. Roberts, “Control chart tests based on geometric moving averages,” Technometrics, vol. 1, no. 3, pp. 239–250, 1959, doi: 10.1080/00401706.1959.10489860.
[12] J. S. Hunter, “The exponentially weighted moving average,” Journal of Quality Technology, vol. 18, no. 4, pp. 203–210, 1986, doi: 10.1080/00224065.1986.11979014.
[13] J. M. Lucas and M. S. Saccucci, “Exponentially weighted moving average control schemes: Properties and enhancements,” Technometrics, vol. 32, no. 1, pp. 1–12, 1990, doi: 10.1080/00401706.1990.10484583.
[14] H. Xie, “Contributions to qualimetry,” Ph.D. dissertation, University of Manitoba, Winnipeg, MB, Canada, 1999.
[15] M. Ahsan, K. A. F. Rifki, M. Mashuri, Wibawati, and M. H. Lee, “Enhanced monitoring of process anomalies: exponentially weighted moving average max multivariate (EWMA Max-M) control chart,” The International Journal of Advanced Manufacturing Technology, vol. 139, no. 9–10, pp. 4441–4455, 2025, doi: 10.1007/s00170-025-16113-6.
[16] P. J. Rousseeuw, “Least median of squares regression,” Journal of the American Statistical Association, vol. 79, no. 388, pp. 871–880, 1984, doi: 10.1080/01621459.1984.10477105.
[17] P. J. Rousseeuw and K. Van Driessen, “A fast algorithm for the minimum covariance determinant estimator,” Technometrics, vol. 41, no. 3, pp. 212–223, 1999, doi: 10.1080/00401706.1999.10485670.
[18] Z. Li, R. Miao, C. Q. Wei, Z. F. Li, and Z. B. Jiang, “A robust MEWMA control chart based on FAST-MCD algorithm,” Advanced Materials Research, vol. 562–564, pp. 1907–1911, 2012, doi: 10.4028/www.scientific.net/AMR.562-564.1907.
[19] F. Fahri, M. Ahsan, and Wibawati, “Simultaneous robust Max-Half-Mchart control charts based on minimum regularized covariance determinant (MRCD),” AIP Conference Proceedings, vol. 3301, no. 1, Art. no. 050008, 2025, doi: 10.1063/5.0262295.
[20] A. P. R. Sembada, M. Ahsan, and Wibawati, “Advanced process monitoring in ordinary portland cement (OPC) data using robust Max-Half-Mchart control charts with Fast-MCD and Det-MCD estimators,” AIP Conference Proceedings, vol. 3301, no. 1, Art. no. 050006, 2025, doi: 10.1063/5.0262293.
[21] A. Javaheri and A. A. Houshmand, “Average run length comparison of multivariate control charts,” Journal of Statistical Computation and Simulation, vol. 69, no. 2, pp. 125–140, 2001, doi: 10.1080/00949650108812086.