Monitoring process variability using auxiliary information

In this study a Shewhart type control chart namely V (r) chart is proposed for improved monitoring of process variability (targeting large shifts) of a quality characteristic of interest Y. The proposed control chart is based on regression type estimator of variance using a single auxiliary variable X. It is assumed that (Y, X) follow a bivariate normal distribution. The design structure of V (r) chart is developed and its comparison is made with the well-known Shewhart control chart namely S-2 chart used for the same purpose. Using power curves as a performance measure it is observed that V (r) chart outperforms the S-2 chart for detecting moderate to large shifts, which is main target of Shewhart type control charts, in process variability under certain conditions on rho(yx) . These efficiency conditions on rho(yx) are also obtained for V-r chart in this study.