An Improved |S| Control Chart for Multivariate Process Variability Monitoring based on Cornish-Fisher Correction

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 correction of the usual normal based 3-sigma limits chart. The exact sample distribution of |S| doesn't have a simple known form for dimension p>2, and we show here that the information from its 3rd and 4th order moments or cumulants are sufficient for a satisfactory approximation. The performance of this corrected control chart is compared (in terms of false alarm risk) with the original normal based chart and the exact distribution based chart (for p=2 and p=3) where in the last case (p=3), the exact distribution is obtained by simulation methods. This study shows that the control limits corrections do remove the drawback of excess of false alarm associated with the traditional normal based |S| control chart. Finally, the proposed new chart is illustrated with a numerical example of application with real data.