Enhancing the Efficiency of CUSUM-Based Location Control Charts Using Robust Statistical Measures

Statistical Quality Control (SQC) involves monitoring and observing goods/industrial procedures to ensure the enhanced quality of goods. Control charts are the primary tools widely valued by businesses for maintaining process consistency. The best standard classes of control charts are the CUSUM charts, also known as the cumulative sum chart. In this work, we propose a novel configuration for CUSUM charts that centers on the use of auxiliary information by a select group of estimators. It involves collective preparation to practice conventional location measures, aiming to improve ratio estimators by utilizing information on auxiliary variables. We have proposed a group of ratio estimators for the population mean in a limited population, utilizing information on auxiliary variables, and employing both conventional and non-conventional measures of location. We have combined the tri-mean, Hodges-Lehmann, mid-range, and decile mean of the auxiliary variables to assist in the purpose. The characteristics related to the suggested group of ratio estimators are estimated using the mean square error. Furthermore, robustness to extreme observations (outliers) is an additional characteristic of the suggested estimators.