Efficieny of estimates of process standard deviation#
Both R-charts and XBar-charts can use sample range to estimate process standard deviation. Estimates of process standard deviation from sample range are less efficient than estimates from sample standard deviation when sample size is greater than two, and those estimates are equal in efficiency when sample size is exactly two (see [1]). Therefore, routines using sample standard deviation might be preferable.
The routines using sample range were written for teaching/learning, for times when interpretation of range is easier than standard deviation, when the simplicity of working with ranges is more important than the loss in efficiency (ie. when drawing charts by hand), and when reproducing older range-based calculations.