An EWMA control chart for the multivariate coefficient of variation

V. Giner Bosch, P. Castagliola

The relative dispersion of a multivariate process can be measured through the multivariate coefficient of variation (MCV). In this talk, we introduce a one-sided control chart for the MCV-squared of a multivariate normal variable based on the well-known exponentially weighted moving average (EWMA) scheme. The limits of the chart are derived using the properties of the underlying probability distribution, a doubly noncentral F distribution, and some challenging mathematical issues are addressed. The performance of our method in terms of its average run length (ARL) is computed by means of Markov chains. Derivative-free numerical algorithms are applied in order to optimally determine the parameters of the chart. We present numerical experiments showing that our proposal outperforms existing alternatives under different settings.

Keywords: statistical process monitoring multivariate coefficient of variation EWMA chart doubly noncentral F distribution

S. Barceló-Cerdá, A. M. Debón Aucejo

M. J. Campuzano Hernández, A. Carrión