Purpose
Rational subgrouping is used to collect data in such a manner as to have the best possible representation of an unknown process state. It's used to separate common-cause from special-cause variation.
Anatomy
Collect Data In Rational Subgroups Whenever Possible
Reference: Douglas C. Montgomery
Terminology
A. True process output measurement of each production unit
B. Individual measurement the subgroup. Usually a sample size of 5 but can me more or less
C. Histogram showing the distribution of the measurement in a subgroup (typical)
D. Subgroups measured in sequence and this sequence must be preserved in the data (typical)
E. Interval between subgroups (rational) in order to capture black noise effects
F. Subgroup sizes (rational) in order to only capture white noise effects
G. Overall measurement distribution (white noise plus black noise)
It is important to note that improper rational subgrouping can lead to the inclusion of special cause effects in the within subgroup variation.
It can also result in missing the non-random variation in the between subgroups variation. The consequence might be a wrong perception of the true situation resulting in inappropriate actions.
Each subgroup (usually consecutive units), must come from a single distinct population. Within subgroup variation should be representative of common-cause only.
The interval between subgroups should be appropriate to capture the between variation due to special causes. Only through a reasonable approach is it possible to obtain rational subgrouping.
Application Cookbook
1. Define the distinct population to be represented by the subgroup data;
2. Establish the minimum subgroup size in order to reflect the within variation;
3. Establish the frequency of the sampling in order to capture the between variation;
4. Collect data maintaining the sequential information.
Donald J. Wheeler has six guiding principles for cllecting data in a rational manner. Keep them in mind when collecting data.
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