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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.
IV.H.3.e
Rules for determining statistical control
Run tests
If the process is stable,
then the distribution of subgroup averages will be approximately normal.
With this in mind, we can also analyze the patterns on the control
charts to see if they might be attributed to a special cause of variation.
To do this, we divide a normal distribution into zones, with each zone
one standard deviation wide. Figure IV.25 shows the approximate percentage
we expect to find in each zone from a stable process.
Figure
IV.25. Percentiles for a normal distribution.
Zone C is the area
from the mean to the mean plus or minus one sigma, zone B is from plus
or minus one to plus or minus two sigma, and zone A is from plus or minus
two to plus or minus three sigma. Of course, any point beyond three sigma
(i.e., outside of the control limit) is an indication of an out-of-control
process.
Since the control limits
are at plus and minus three standard deviations, finding the one and two
sigma lines on a control chart is as simple as dividing the distance between
the grand average and either control limit into thirds, which can be done
using a ruler. This divides each half of the control chart into three
zones. The three zones are labeled A, B, and C as shown on Figure IV.26.
Figure
IV.26. Zones on a control chart.
Based on the expected
percentages in each zone, sensitive run tests can be developed for analyzing
the patterns of variation in the various zones. Remember, the existence
of a non-random pattern means that a special cause of variation was (or
is) probably present. The averages, np and c control chart
run tests are shown in Figure IV.27.
Figure
IV.27. Tests for out of control patterns on control charts.
From
"The Shewhart Control Chart–Tests for Special Causes,"
Journal of Quality Technology, 16(4), p 238. Copyright © 1986
by Nelson.
Note that, when a point
responds to an out-of-control test it is marked with an "X"
to make the interpretation of the chart easier. Using this convention,
the patterns on the control charts can be used as an aid in troubleshooting.
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