Correction on link relative based approach to CUSUM chart

Link relative-based approach was used in an article (see reference 1) to enhance the performance of the cumulative sum (CUSUM) control chart. This technique involves the use of firstly, the link relative variable to convert the process observations in a relative to the mean form and secondly, optimal constants to define a new variable which is used as the plotting statistic of the link relative CUSUM chart. In this article, it is proven through simulation study that the optimal constants with fixed values, as reported in the aforementioned article, give different results. Instead, if the regression technique is used, then the same results will be obtained.