Interpretation & Calculations
An excerpt from Statistical Process Control Demystified (McGraw-Hill 2011) by Paul Keller.
The key to successful control charts is the formation of rational subgroups. Control charts rely upon rational subgroups to estimate the short-term variation in the process. This short-term variation is then used to predict the longer-term variation defined by the control limits, which differentiate between common and special causes of variation.
A rational subgroup is simply a sample in which all of the items are produced under conditions in which only random effects are responsible for the observed variation (Nelson, Lloyd S. "Control Charts: Rational Subgroups and Effective Applications," Journal of Quality Technology. Vol. 20, No. 1, January 1988). Another way to express this is that a rational subgroup is one in which the system of causes influencing within subgroup variation is equivalent to the system of causes influencing between subgroup variation.
A rational subgroup has the following properties:
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).