An EWMA mean chart with auxiliary information

Abstract

AbstractIn this paper, we show that a recently proposed auxiliary information‐based (AIB) adaptive EWMA (AE) chart is sensitive (not robust) to the changes in the mean of an auxiliary variable when monitoring the changes in the mean of a quality variable, called the AIB‐AE chart. To circumvent the weakness of the AIB‐AE chart, we develop a new AIB estimator for the mean of a quality variable that is slightly robust to the changes in the mean of an auxiliary variable. Based on this newly developed estimator, a new AIB EWMA (AIB‐E) chart is proposed for monitoring the mean of a quality variable. The zero‐state and steady‐state average run‐length profiles of the AIB‐AE and AIB‐E charts are estimated with Monte Carlo simulations. It is found that the AIB‐E chart is not only slightly robust to the changes in the mean of an auxiliary variable, but it also outperforms the AIB‐AE chart when detecting small shifts in the mean of a quality variable. Illustrative examples are also included in this study to demonstrate the implementation of the existing and proposed AIB charts.