Adaptive sample size control charts for attributes

Abstract

Theoretical results have shown that the X̄ chart with variable sample sizes (VSS) is quicker than the traditional X̄ chart for detecting moderate shifts in the process. The idea is to make the sample size vary depending on what is observed from the process. If the current X̄ value is far from the target (centerline), but not far enough to produce a signal, the control is tightened by making the next sample larger than usual. On the other hand, if the current X̄ value is near the target, the control is relaxed by making the next sample smaller than usual. The VSS scheme does not increase the rate of inspected items because the large samples are always compensated by the small ones. This article adds the VSS feature to control charts for attributes. The VSS np and c charts' properties are obtained using Markov chains. The gain in speed with which these charts detect process deterioration (that increases the number of defectives or defects during production) is worth of study.