An attribute chart for monitoring the process mean and variance

Abstract

This article proposes an attribute chart for variables (AFV chart) that employs an attribute inspection (checking whether a unit is conforming or nonconforming) to monitor not only the mean but also the variance of a variable x. The salient feature of the AFV chart is its ability to determine the process status (i.e. in control or out of control) by applying the very simple attribute inspection to a single unit. By selecting its inspection limits appropriately, the AFV chart usually outperforms the joint & R and & S charts from an overall viewpoint under different circumstances. The AFV chart has the advantage of being extremely simple in design and implementation, and having a very low cost for operation. In particular, the AFV chart uses a single-attribute inspection for each sample, works as a leading indicator of trouble and allows operators to take the proper corrective action before any defective is actually produced. Since the AFV chart is simpler, more effective and less costly than the & R and & S charts, it may be highly preferred for many statistical process control applications, in which both the mean and variance of a variable need to be monitored.