Rational Sub Grouping

If you want to operate control charts in a successful manner, the most important thing that you need to know is the formation of rational subgroups. Rational subgroups help in the estimation process of the short term variations for control charts. These variations later help us predict the long term variations and their control limits, depending o the type of causes for the variation (special or common).

Rational subgroups are samples in which we produce all of the items under conditions which will only occur in the presence of random effects (which can then be held responsible for the observed variations). This has been stated quite eloquently in Nelson, Lloyd S. “Control Charts: Rational Subgroups and Effective Applications,” Journal of Quality Technology. Vol. 20, No. 1, January 1988. In other terms, a rational group is the one in which the influence causing system within the variation of the subgroup is approximately the same as the system of causes influencing between subgroup variation.

A rational subgroup is said to possess the following properties:

  • The observations within a subgroup come from a lone steady process. If the subgroup instead has multiple process elements in it or if it has other special causes that occur at high frequency within the sub group, then the variation within the subgroup will be quite high when compared to the variation between the averages of the subgroups. Such large diversities within the subgroups pushes the control limits too far away and thus results in a total lack of sensitivity to the shifting processes. This can be detected using the Western Electric Run Test 7 (15 successive points within one sigma of center line)
  • The subgroups are all formed from the observations that have been taken in a sequence that has been time-ordered. Simply speaking, subgroups are never formed randomly from a set of available data; it is not that simple. The data is supposed to be a “snapshot” of the process over a very small amount of time and the sequence that we set them in will depict how these snapshots will vary over some specified time. Think of it like a picture frame in a movie. The picture frame is not understandable on its own but it is a vital part of the movie when it is run. The amount of time we need for the snapshot depends on individual processes. We avoid using a general rule to reduce the risk of a special chance that may occur within a group.
  • The observations within the subgroups are autonomous, which means that no observation influences, or results from, another. If in some case the observations do depend on one another, than the process is said to have autocorrelation (also known as serial correlation). In many cases, the autocorrelation causes the within subgroup variation to be unusually small and a poor analyst of the between subgroup variation. The small within subgroup variation forces the control limits to be too narrow, resulting in frequent out of control conditions.
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