New efficient exponentially weighted moving average variability charts based on auxiliary information

Abstract

Control chart is a well-known tool for monitoring the performance of an ongoing process. The variability of a process is an important parameter that may deteriorate the process performance if it is not taken care on time. In this study, we have proposed some new auxiliary information-based exponentially weighted moving average (EWMA) charts for improved monitoring of process variability. We employed auxiliary information in some useful forms including ratio, regression, power ratio, ratio exponential, ratio regression, power ratio regression, and ratio exponential regression estimators. The performance of the newly developed charts is evaluated and compared with some existing charts (viz., the NEWMA, the Improved R, the Synthetic R, and the classical R charts), using some useful measures such as average run length (ARL), extra quadratic loss, and relative ARL. The comparative analysis revealed that the proposed charts outperform their counterparts, especially when there is a strong relationship between the study and the auxiliary variables. Finally, an illustrative example is provided for the monitoring of air quality data