On the Properties of the Rank Based Multivariate Exponentially Weighted Moving Average Control Charts

Abstract

The rank based multivariate exponentially weighted moving average (rMEWMA) control chart was proposed by Messaoud et al. (2005). It is a generalization, using the data depth notion, of the nonparametric EWMA control chart for individual observations proposed by Hackl and Ledolter (1992). The authors approximated its asymptotic in-control performance using an integral equation and assuming that a sufficiently large reference sample is available. The actual paper studies the effect of the use of reference samples of limited amount of observations on the in-control and out-of-control performances of the proposed control chart. Furthermore, general recommendations for the required reference sample sizes are given so that the in-control and out-of-control performances of the rMEWMA control chart approach their asymptotic counterparts.