Cumulative conformance count charts with variable sampling intervals for correlated samples

Abstract

The cumulative conformance count (CCC) control chart is often employed to monitor the fraction nonconforming of high-yield processes. Traditional CCC chart is used when the items from a process are inspected one-at-a-time following the production order. In recent years, the CCC chart has been generalized to accommodate some industrial practices where items from a process are inspected sample by sample and not according to the production order. In order to increase the sensitivity of the generalized CCC (GCCC) chart to changes in fraction nonconforming, the variable sampling interval (VSI) scheme is used in this study. The output characteristic within each sample is assumed with correlation. The statistical properties of the GCCC chart with the VSI scheme are deduced using the Markov chain method. In evaluating the usefulness of the VSI feature, GCCC charts with VSI and fixed sampling interval (FSI) schemes are compared in terms of their statistical properties. The comparison results show that using the VSI scheme can improve the speed of GCCC chart in detecting changes in fraction nonconforming. Finally, according to the comparison results, a design procedure is applied to an industrial example to validate its practicability.