A Study of Shewhart Control Charts Using Robust Measures

Statistical Quality Control (SQC) is a structured methodology used to monitor, evaluate, and control industrial production processes to maintain consistent product quality and operational efficiency. Control charts are essential tools widely utilized in business to maintain process variability within acceptable limits. The CUSUM chart is the most effective standard type of control chart, serving as a memorial chart. This study proposes a novel configuration for CUSUM Charts based on the utilization of auxiliary information through a limited number of estimators. It is a collaborative effort to implement traditional location measures to enhance ratio estimators using auxiliary variable information. We have proposed a set of ratio estimators for finite population mean utilizing information from auxiliary variables through both standard and unconventional measures of central tendency. We have amalgamated the tri-mean, Hodges-Lehmann estimator, mid-range, and deciles mean of the auxiliary variables to facilitate the objective. The attributes associated with the proposed set of ratio estimators are evaluated using mean square error. Moreover, resilience to extreme observations (outliers) is an additional attribute of the proposed estimators.