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Multivariate EWMA charts with accumulate-combine method for multivariate normal process
Journal of the Korean Data & Information Science Society 2020;31:51-63
Published online January 31, 2020;
© 2020 Korean Data and Information Science Society.

Duk-Joon Chang1

1Department of Statistics, Changwon National University
Correspondence to: Professor, Department of Statistics, Changwon National University, Changwon 51140, Korea. E-mail:
This research was supported by Changwon National University in 2019∼2020.
Received December 31, 2019; Revised January 8, 2020; Accepted January 8, 2020.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This research presents three multivariate EWMA (exponentially weighted moving average) charts using accumulate-combine method to control simultaneously both mean vector µ and variance-covariance matrix Σ, which are parameters of multivariate normal process Np(µ, Σ) with p (p ≥ 2) quality characteristics, and presents the 3-chart combining procedure which combines the three multivariate EWMA charts to one chart. In addition, this research also shows the numerical performances of the 3-chart combining procedure using simulation works. Simulation results shows that the multivariate EWMA chart using accumulate-combine method is more effective than the multivariate EWMA chart using combine-accumulate method, and that the multivariate EWMA chart with small smoothing constant λ is more sensitive to smaller shift. Especially, in case of interests of the change of correlation coefficients of quality variables both the multivariate Shewhart chart and the EWMA chart based on control statistic Di are not recommendable for detecting the process changing.
Keywords : Accumulate-combine method, ANSS, ARL, combine-accumulate method, 3-chart combining procedure.