A phase II multivariate EWMA chart for monitoring multi-dimensional ratios of process means with individual observations

In recent years, there has been a resurgence in the development of control charts for monitoring the mean of the ratio of two correlated variables. However, most of the existing research has focused on the univariate mean of the ratio of two correlated variables under the assumption that the process follows a bivariate normal distribution. Furthermore, most of the existing research utilize biased estimators of the mean of the ratio of two correlated variables to develop control charts. More importantly, in certain applications, critical quality characteristics to be closely monitored are actually the ratios of the means of correlated variables, in that the process is considered to be stable as long as the ratios of the means of correlated variables remain constant at given levels, regardless of how each variable changes. We are thus motivated in this study to develop an exponentially weighted moving average (EWMA) based Phase II control chart for monitoring multi-dimensional ratios of the means of correlated variables. In this study, we provide a general framework for estimating parameters and control limits which is applicable without having to assume that the process follows a multivariate normal distribution. The performance of the proposed chart is evaluated under different multivariate distributions. Finally, a real data application of the proposed chart is presented to illustrate the practicality of the proposed chart.