Rational Subgroups

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:

The observations within a subgroup are from a single, stable process. If subgroups contain the elements of multiple process streams, or if other special causes occur frequently within subgroups, then the within subgroup variation will be large relative to the variation between subgroup averages. This large within subgroup variation forces the control limits to be too far apart, resulting in a lack of sensitivity to process shifts. Western Electric Run Test 7 (15 successive points within one sigma of center line) is helpful in detecting this condition.
The subgroups are formed from observations taken in a time-ordered sequence. In other words, subgroups cannot be randomly formed from a set of data (or a box of parts); instead, the data comprising a subgroup must be a "snapshot" of the process over a small window of time, and the order of the subgroups would show how those snapshots vary in time (like a "movie"). The size of the "small window of time" is determined on an individual process basis to minimize the chance of a special cause occurring in the subgroup.
The observations within the subgroups are independent, implying that no observation influences, or results from, another. If observations are dependent on one another, the process has autocorrelation (also known as serial correlation). In many cases, the autocorrelation causes the within subgroup variation to be unnaturally small and a poor predictor 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, leading to the tampering discussed in Chapter 1. Many examples of autocorrelation exist in business processes and nature itself including:

Chemical Processes: Samples drawn from liquids in batches are often influenced by prior samples if the time between the samples is small. The batch is essentially homogenous throughout, and its properties change slowly so that the measurement at one point in time is influenced by the state of the process in an earlier state of time.
Service Processes: The wait time of a person in a queue is influenced by the wait time of the person in front of him/her. Recall your wait time at the supermarket check out line when you're behind a chatty customer: You cannot be serviced until their service is completed; likewise for the person behind you, and so on.
Discrete part manufacturing: Feedback controls used to adjust processes based upon past observations cause autocorrelation in data observed closely in time.

See further discussion of rational subgroups.

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).