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MCMAX control chart for the joint monitoring of the mean vector and the covariance matrix

The control chart and the generalized variance |S| chart are used for monitoring the mean vector and the covariance matrix of multivariate processes. In this article, we propose the use of a single chart for monitoring bivariate processes, that is, the MCMAX control chart based on a new statistic, which corresponds to the maximum among four sample values: the standardized sample means (in module) and the standardized sample variances (weighted). The sample means and sample variances are well known by the users; the same cannot be said for the Hotelling's statistic or the generalized variance. Consequently, they will prefer to use the proposed chart instead of the joint and |S| charts. In general, the user prefers to wait until the occurrence of a second point beyond the control limit (not far from the first one) before interfering in the process. With this new rule, the proposed chart is faster in signaling out-of-control conditions, except when the correlation between the two quality characteristics is too high. In this case, the joint and |S| charts are faster is signaling assignable causes that only affect one of the two quality characteristics, changing its mean and/or increasing its variance.

MCMAX control chart; Covariance matrix; Mean vector; Bivariate processes; Special run rule

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