A control scheme for monitoring process covariance matrices with more variables than observations

In this paper, we propose a new control chart that integrates a powerful highdimensional covariance matrix test with the exponentially weighted moving average procedure for monitoring high-dimensional variability with individual observations. Design and implementation of the proposed chart are provided, including search algorithm and a table for the control limits, diagnostic aids after the signal, effect of misspecifying the in-control distribution and a bootstrap procedure. Monte-Carlo simulation results show that the new chart, with its powerful inherited properties, provides satisfactory performance in various cases, especially for covariance shifts that involve diagonal components. The application of the proposed method is illustrated with a real data example from a white wine production process.

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