The non-central chi-square chart with two-stage samplings

In this paper, we consider the non-central chi-square chart with two stage samplings. During the first stage, one item of the sample is inspected and, depending on the result, the sampling is either interrupted, or it goes on to the second stage, where the remaining sample items are inspected and the non-central chi-square statistic is computed. The proposed chart is not only more sensitive than the joint X and R charts, but operationally simpler too, particularly when appropriate devices, such as go–no-go gauges, can be used to decide if the sampling should go on to the second stage or not.