The effect of shift distribution on the design and performance of the X and CUSUM charts in monitoring mean and variability

When monitoring a variable x in statistical process control, it is necessary to monitor both the mean and variability. Recently, it is found that, if both the mean shift δμ and standard deviation shift δσ follow the uniform distribution, many control charts with different complicacy are equally or similarly effective. This is referred as a performance equality property. However, the real distributions of δμ and δσ may not be uniform and the determination of these real distributions is very difficult. This article has shown that the control charts designed optimally based on the assumed uniform distributions of δμ and δσ are almost as effective as the charts designed based on the real distributions. Moreover, even if and follow non-uniform distributions, the performance equality property still holds. These results confirm that the optimisation design is an effective way to improve chart performance for any distributions of δμ and δσ. [Received 11 March 2011; Revised 13 August 2011; Accepted 18 September 2011].