Variable sampling interval EWMA chart for multivariate coefficient of variation

Abstract

A control chart for monitoring the multivariate coefficient of variation (MCV) is used when the focus is on monitoring the ratio of relative multivariate variability to the mean of a multivariate process. The MCV chart is useful in process monitoring when practitioners are not interested in the consistency of the mean vector or covariance matrix. This study proposes a one-sided upward variable sampling interval (VSI) exponentially weighted moving average (EWMA) chart to detect increasing shifts in MCV squared $({\mathrm{\gamma }}^2)$ and shows the derivation of formulae to evaluate the performance of the VSI EWMA-${\mathrm{\gamma }}^2$ chart by using the Markov chain approach. Comparative investigations show that the proposed chart outperforms existing MCV charts in detecting shifts in process MCV. A numerical example that uses real data reveals that the proposed chart performs well in actual applications.

Keywords:

• Exponentially weighted moving average
• multivariate coefficient of variation
• variable sampling interval
• average time to signal
• expected average time to signal
• standard deviation of the time to signal

Additional information

Funding

This research was supported by the Kementerian Pendidikan Malaysia, Fundamental Research Grant Scheme, number 203.PMATHS.6711603.