On designing CUSUM charts using ratio-type estimators for monitoring the location of normal processes

A control chart is an important tool in statistical process control that plays a signicant role in monitoring and identifying variations in production processes. The Shewhart, the cumulative sum (CUSUM), and the ExponentiallyWeighted Moving Average (EWMA) control charts are commonly used for detecting process shifts. The CUSUM and the EWMA control charts are more sensitive in detecting smaller shifts, whereas the typical Shewhart chart is sensitive to large process shifts. The present study incorporates ratiotype estimators of the population mean based on auxiliary information in the CUSUM charting structure for monitoring the location of the normal processes. These estimators are more ecient than simple mean estimator in the presence of a high correlation between the study and the auxiliary variables. The Average Run Length (ARL), the standard deviation of run length, and the extra quadratic loss are used to measure the performance of the proposed charts. The proposed charts are compared with the existing CUSUM, CUSUM-FIR, and some other auxiliary information-based control charts on the basis of out-of-control ARLs. The comparison reveals the superiority of the suggested charts over the other existing charts. An illustrative example is also provided for the performance evaluation of the proposed charts.