**AUTHORS:**Yuma Ueno, Masato Ohkubo, Yasushi Nagata

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**ABSTRACT:**
This study aims to detect various small changes in multivariate control charts. In previous studies, the
MEWMA control chart was proposed as a detection of mean vector change, the MEWMC control chart was
proposed as a detection of variance covariance matrix change, and the ELR control chart was proposed as a
detection of the change of the mean vector and the variance covariance matrix. This study proposes two method
using log-likelihood. The first method (MEWML control chart) uses the statistic obtained by directly weighting
the log-likelihood. The second method (MEWMML control chart) uses obtained maximum likelihood estimate
from log-likelihood using the maximum likelihood method. As a result of Monte Carlo simulations using the
ARL evaluation index, the study shows that the MEWML control chart is useful for variance covariance matrix
change, and the MEWMML control chart is the most useful for various patterns.

**KEYWORDS:**
MEWMA, multivariate control chart, log-likelihood, maximum likelihood method, MEWMC, ARL

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