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 &chi;2 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<br />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<br />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<br />T value falls above the upper control limit of the proposed chart. The DS &chi;2 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 &chi;2 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.