$|S|$ Control Chart for Multivariate Process Variability Monitoring Based on Cornish-Fisher Correction and Meijer-G Function

This paper presents an improved version of the generalized variance |S| control chart for multivariate process dispersion monitoring, based on the Cornish-Fisher formula for non-normality correctionof the normal based 3-sigma chart limits. Also, the exact sample distribution of |S| and its quantiles (chart exact limits) are obtained through the Meijer-G function, and an auxiliary control chart basedon the trace of V (standardized S matrix) is introduced. The performance of this corrected control chart is compared (in terms of false alarm risk) with the traditional normal based chart and the exactdistribution based chart (for dimensions d = 2 and d = 3). This study shows that the control limits corrections do remove the drawback of excess of false alarm associated with the traditional normalbased |S| control chart. The proposed new chart is illustrated with two numerical examples.