Th e Non-Central Chi-Square Chart with Double Sampling

Abstract

In this article, we consider a non-central chi-square chart with double sampling (DS χ2 chart) to control the process mean and variance. As in the case of Shewhart control charts, samples of fi xed size are taken from the process at regular time intervals; however, the sampling is performed in two stages. Let X be the process quality variable being measured. During the fi rst stage, one item of the sample is inspected; if its X value is close
to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and a
non-central chi-square statistic, say T, is computed taking into account all n items of the sample, that is, their X values. A signal is triggered when the sample point given by the
T value falls above the upper control limit of the proposed chart. The DS χ2 chart performs better than the joint X and R charts, except when there is a large change in the process mean. Furthermore, if the DS χ2 chart is used for monitoring diameters, volumes, weights, etc., then the employment of appropriate devices, such as go-no-go gauges can reduce the effort to decide if the sampling should go to the second stage or not.