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The following
is an excerpt from Chapter 4 of The
Quality Engineering Handbook by Thomas
Pyzdek, © Quality Publishing. It may be ordered from the Quality
Publishing Order Form
Rational
subgroup sampling
The basis of all control
charts is the rational subgroup. Rational subgroups are composed of items
which were produced under essentially the same conditions. The statistics,
for example, the average and range, are computed for each subgroup separately,
then plotted on the control chart. When possible, rational subgroups are
formed by using consecutive units. Each subgroup’s statistics are
compared to the control limits, and patterns of variation between subgroups
are analyzed. Note the sharp contrast between this approach and the random
sampling approach used for enumerative statistical methods.
The idea of rational subgrouping
becomes a bit fuzzy when dealing with x charts, or individuals control
charts. The reader may well wonder about the meaning of the term subgrouping
when the "subgroup" is a single measurement. The basic idea
underlying control charts of all types is to identify the capability of
the process. The mechanism by which this is accomplished is careful formation
of rational subgroups as defined above. When possible, rational subgroups
are formed by using consecutive units. The measure of process variability,
either the subgroup standard deviation or the subgroup range, is the basis
of the control limits for averages. Conceptually, this is akin to basing
the control limits on short-term variation. These control limits are used
to monitor variation over time.
As far as possible, this
approach also forms the basis of establishing control limits for individual
measurements. This is done by forming quasi-subgroups using pairs of consecutive
measurements. These "subgroups of 2" are used to compute ranges.
The ranges are used to compute the control limits for the individual measurements.
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