A process variability control chart

In this study a Shewhart type control chart namely the Vt chart, is proposed
for improvedmonitoring of the process variability of a quality characteristic of interest
Y . The proposed control chart is based on the ratio type estimator of the variance
using a single auxiliary variable X. It is assumed that (Y, X) follows a bivariate normal
distribution. The design structure of the Vt chart is developed for Phase-I quality control
and its comparison is made with those of the S2 chart (a well-known Shewhart control
chart) 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 outperforms
the S2 and Vr charts, in terms of discriminatory power, for detecting moderate to large
shifts in the process variability. It is observed that the performance of the Vt chart
keeps improving with an increase in pyx, where ρyx is the correlation between Y
and X.