Combined charts for mean and variance information

Since the earliest days of statistical process control, it has been recognized that it is essential to monitor both mean and variability and to sound an alarm if either of these characteristics shows sign of a special cause. Traditionally, this has been done by using separate X̄ and S charts, with the implication that if either chart exceeds its control limit action will be taken to diagnose and resolve any special causes. It is, however, possible to monitor both mean and variance in a single chart responsive to shifts in either, and several proposals along these lines have been published. Two new combination charts are proposed, and it is shown that, in addition to the simplicity of a single chart rather than two, a combination chart may have significant performance advantages over the X̄ and S chart pair. Good practice augments the traditional Shewhart charts with cumulative sum or exponentially weighted moving average charts for location and for scale; these pairs may also be replaced by combination charts.