A process variability control chart

Abstract

In this study a Shewhart type control chart namely the Vt chart, is proposedfor improvedmonitoring of the process variability of a quality characteristic of interestY . The proposed control chart is based on the ratio type estimator of the varianceusing a single auxiliary variable X. It is assumed that (Y, X) follows a bivariate normaldistribution. The design structure of the Vt chart is developed for Phase-I quality controland its comparison is made with those of the S2 chart (a well-known Shewhart controlchart) and the Vr chart (a Shewhart type control chart proposed by Riaz (Comput Stat,2008a) used for the same purpose. It is observed that the proposed Vt chart outperformsthe S2 and Vr charts, in terms of discriminatory power, for detecting moderate to largeshifts in the process variability. It is observed that the performance of the Vt chartkeeps improving with an increase in pyx, where ρyx is the correlation between Yand X