Using one EWMA chart to jointly monitor the process mean and variance

Two control charts are usually used to monitor the process mean and variance separately. The mean is monitored using the `(X)]{\bar{{X}}} chart while the variance using either the standard deviation, S chart, or the range, R chart. Recently, numerous single variable charts are proposed to jointly monitor the mean and variance. Most approaches transform the sample mean and sample variance into two statistics, each having a standard scale, and either plotting them on the same chart or combining them into a single statistic to be plotted on a chart. The R chart is more widely used than the S chart but no attempt is made to combine the `(X)]{\bar{{X}}} and R charts in the construction of a single variable chart and to study its properties and performance. In this paper, we transform the `(X)]{\bar{{X}}} and R statistics into two standard normal random variables, used in the computation of two corresponding exponentially weighted moving average (EWMA) statistics, which are then merged into a single plotting statistic for the proposed chart, called the EWMA `(X)]-R{\bar{{X}}-R} chart.