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

Abstract

A control chart is an important tool in statistical process control that plays a signi cant role in monitoring and identifying variations in production processes. The Shewhart, the cumulative sum (CUSUM), and the Exponentially Weighted 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 e cient 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.

Enhancing the efficiency of the ratio-type estimators of population variance with a blend of information on robust location measures

“…When auxiliary information is available and the study variable is positively correlated with the auxiliary variable, the ratio estimation method is frequently used to improve the efficiency of the estimators of population characteristics [2]. The ratio-type estimators are now being frequently used in different fields such as process monitoring, designing of acceptance sampling plan for lot sentencing, environmental studies, and forestry are few to mention [3][4][5][6][7][8]. Generally, the information of conventional auxiliary parameters such as the coefficient of kurtosis, the coefficient of skewness, the coefficient of variation, and the coefficient of correlation is used in a linear combination with the sample information of the study and the auxiliary variable to design the estimators of population variance.…”