A new chart based on sample variances for monitoring the covariance matrix of multivariate processes

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Costa, A. F. B. [UNESP]
Machado, M. A. G. [UNESP]

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Springer London Ltd


In this article, we propose a control chart for detecting shifts in the covariance matrix of a multivariate process. The monitoring statistic is based on the standardized sample variance of p quality characteristics we call the VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these p variances. The reasons to consider the VMAX statistic instead of the generalized variance |S| are faster detection of process changes and better diagnostic features, which mean that the VMAX statistic is better at identifying the out-of-control variable. User's familiarity with sample variances is another point in favor of the VMAX statistic. An example is presented to illustrate the application of the proposed chart.



Control charts, Multivariate processes, Covariance matrix, Generalized variance

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International Journal of Advanced Manufacturing Technology. Artington: Springer London Ltd, v. 41, n. 7-8, p. 770-779, 2009.