An EWMA mean chart with auxiliary information

In 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.