Increasing the sensitivity of cumulative sum charts for location

Abstract

The cumulative sum (CUSUM) chart is a very effective control charting procedure used for the quick detection of small-sized and moderate-sized changes. It can detect small process shifts missed by the Shewhart-type control chart, which is sensitive mainly to large shifts. To further enhance the sensitivity of the CUSUM control chart at detecting very small process disturbances, this article presents CUSUM control charts based on well-structured sampling procedures, double ranked set sampling, median-double ranked set sampling, and double-median ranked set sampling. These sampling techniques significantly improve the overall performance of the CUSUM chart over the entire process mean shift range, without increasing the false alarm rate. The newly developed control schemes do not only dominate most of the existing charts but are also easy to design and implement as illustrated through an application example of real datasets. The control schemes used for comparison in this study include the conventional CUSUM chart, a fast initial response CUSUM chart, a 2-CUSUM chart, a 3-CUSUM chart, a runs rules-based CUSUM chart, the enhanced adaptive CUSUM chart, the CUSUM chart based on ranked set sampling (RSS), and the single CUSUM and combined Shewhart-CUSUM charts based on median RSS