An X and EWMA chart for individual observations

While there is much experience in monitoring processes with individual observations it is not clear which procedure is best. We compare individual observation control procedures that are combinations of the moving range (MR), exponentially weighted moving average (EWMA), and X charts, with and without run rules. We estimate the average run length (ARL) to false alarms and to detection of shifts in the process mean and standard deviation using simulation. Our recommendation is the X and EWMA chart, a practical method in that both charts are plotted in a single, easily interpreted graph. It detects large and small shifts in the process mean and large shifts in the process standard deviation.