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Properties of VSI EWMA chart combined three accumulate-combine multivariate charts
Journal of the Korean Data & Information Science Society 2021;32:953-68
Published online September 30, 2021;
© 2021 Korean Data and Information Science Society.

Duk-Joon Chang1

1Department of Statistics, Changwon National University
Correspondence to: 1 Professor, Dept. of Statistics, Changwon National University, Changwon 51140, Korea.
This research was supported by Changwon National University in 2021∼2022.
Received August 9, 2021; Revised September 17, 2021; Accepted September 17, 2021.
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.
In a multivariate normal process Np(μ, Σ) with p (p ≥ 2) quality characteristics, a combined chart with its control statistics is suggested, which combines three multivariate EWMA (exponential weighted moving average) charts, each chart for monitoring respectively elements of mean vector, variance components of dispersion matrix, and off-diagonal elements of dispersion matrix, using accumulated-combine method. The combined FSI (fixed sampling interval) chart is extended to VSI (variable sampling interval) chart, and the numerical properties of VSI EWMA chart is examined using simulation. Simulation results show that the suggested chart is very effective for small change of the process parameters of miltivariate normal process. And the suggested chart is more effective at the small shift of process, and ATS and ANSS are smaller, as the smoothing constant is smaller. In addition, ANSW and switch probability, which are main properties of VSI charts, also tend to get smaller at small smoothing constant.
Keywords : Accumulate-combine method, ANSW, ATS, EWMA chart, VSI.