Extending a double sampling control chart for non-conforming proportion in high quality processes to the case of small samples

When production processes reach high quality standards they are known as high quality processes. In this situation, the conventional $p$ charts (based on 3-sigma limits) used for monitoring non-conforming products have serious drawbacks in detecting changes in $p$ due to excess of false alarm risk. In a previous paper, the authors showed a new $p$ chart that provides a large improvement over the usual $p$ chart in these situations. In this paper, authors propose a new corrected version of a double sampling (DS) control chart for monitoring the proportion $p$ of non-conforming presented in the literature for large samples, in order to extend its applicability to the case of small samples. This procedure offers better statistical efficiency (in terms of the average run length) than the previous $p$ charts, without increasing the sampling. Tables are provided to aid in the choice of DS parameters. The benefits of the corrected version of a DS chart for monitoring high-quality processes are illustrated with real data.