Enhanced memory-type charts for monitoring the ratio of two normal random variables

Abstract

It is common in the SPC literature to enhance the sensitivity of a control chart using an auxiliary information based estimator of the underlying process parameter(s) that requires information on the study variable, as well as supplementary information on one or more auxiliary variables. In this study, we develop a novel approach to monitor the ratio of two normal means when the underlying process follows a multivariate normal distribution. Under the proposed setup, to monitor the process ratio, the supplementary information can be utilized on one or more auxiliary variables. In addition, we propose the EWMA and CUSUM charts for monitoring the process ratio of the means. Using Monte Carlo simulations, the run length profiles of these control charts are computed, and then evaluated in terms of the run length properties. It is found that the proposed charts may uniformly and substantially outperform the existing charts when detecting upward and downward shifts simultaneously in the process ratio of the means. A real dataset is also considered to demonstrate the implementation of existing and proposed charts.