Detecting improvement using Shewhart attribute control charts when the lower control limit is zero

In this paper, we present a method to monitor count data so as to be able to detect improvement when the counts are low enough to cause the lower limit to be zero. The method, which is proposed as an add-on to the conventional Shewhart control chart, consists in counting the number of samples in which zero defectives or zero defects per unit occur and signaling an increase in quality if k-in-a-row or 2-in-t samples have zero counts of defectives or zero defects per unit. This method enjoys some similarities to the very popular Shewhart control chart in that it is easy to design, understand and use. It is flexible, robust, and, like the Shewhart chart, yields detection frequencies that are optimal for very large shifts and good for other shifts. Some comparisons with traditional CUSUM charts are provided. Figures enabling Shewhart control chart users to easily design low-side add-on control charts are given for c and np charts.