Combined Charts for Mean and Variance Information

AbstractSince 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 Ū 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 Ū 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.KeywordsFisher MethodsLikelihood RatioShewhart Control Charts Additional informationNotes on contributorsDouglas M. HawkinsDr. Hawkins is Professor, School of Statistics, University of Minnesota, and is an ASQ Fellow. His email is dhawkins@umn.edu.Qiqi DengDr. Deng is a Senior Biostatistician, Boehringer Ingelheim Pharmaceuticals. Her email is qiqi.deng@boehringer-ingelheim.com.