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Interpreting
an Individual-X / MR Chart
Always look at Moving Range
chart first. The control limits on the Individual-X chart are derived from
the average moving range, so if the Moving Range chart is out of control,
then the control limits on the Individual-X chart are meaningless. (However,
research has shown that for Normally distributed processes, when a Special
Cause is detected on the Moving Range Chart, it will also appear on the
Individual-X chart, thus making the Moving Range chart redundant. See for example
Design Strategies for Individuals and Moving Range Control Charts, Rigdon, Cruthis, & Champ,
Journal of Quality Technology: Vol. 26, No. 4, October 1994.)
After reviewing the Moving
Range chart, interpret the points on the Individual-X chart relative to
the control limits and Run Tests. Never consider the points on the Individual-X
chart relative to specifications, since this tampering will increase the
overall variation in the process. See also: Tampering
.
Interpreting the Moving
Range Chart
On
the Moving Range chart, look for out of control points. If there are any,
then the special causes must be eliminated. Brainstorm and conduct Designed
Experiments to find those process elements that contribute to sporadic changes
in variation. To use the data you have, turn Auto Drop ON, which will remove
the statistical bias of the out of control points by dropping them from
the calculations of the average Moving Range, Moving Range control limits,
average Individual-X and Individual-X control limits.
Also on the moving range
chart, there should be more than five distinct values plotted, and no one
value should appear more than 25% of the time. If there are values repeated
too often, then you have inadequate resolution of your measurements, which
will adversely affect your control limit calculations. In this case, you'll
have to look at how you measure the variable, and try to measure it more
precisely.
Once you've removed the
effect of the out of control points from the Moving Range chart, look at
the Individual-X Chart.
Interpreting the Individual-X
Chart
After
reviewing the Moving Range chart, look for out of control points on the
Individual-X Chart. If there are any, then the special causes must be eliminated.
Brainstorm and conduct Designed Experiments to find those process elements
that contribute to sporadic changes in process location. To use the data
you have, turn Auto Drop ON, which will remove the statistical bias of the
out of control points by dropping them from the calculations of the average
Individual-X and Individual-X control limits.
Look for obviously non-random
behavior. Turn on the Run Tests, which apply statistical tests for trends
to the plotted points.
An important consideration
for the Individual-X Chart is the choice of Curve Fit used for determining
the control limits. There is a fundamental problem here, in that a distribution
should not be fit to the data unless the data is from a controlled process.
Unfortunately, you may need to fit a distribution to the data to effectively
use the Individual-X chart to determine if the process is in control. Because
of this limitation, you may consider using other control charts, such as
the X-bar Chart or EWMA chart to first define process control. See also:
SPC Concepts , Distributions
, Defining Control Limits
If the process shows control
relative to the statistical limits and Run Tests for a sufficient period
of time (long enough to see all potential special causes), then we can analyze
its capability relative to requirements. Capability is only meaningful when
the process is stable, since we cannot predict the outcome of an unstable
process. See also: Interpreting
the Run Tests, Process
Capability Charts
See also:
When
to Use an Individual-X Chart
Individual-X
Chart Calculations
Moving
Range Chart Calculations
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