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# Interpreting an X-bar / R Chart

Always look at the Range chart first. The control limits on the X-bar chart are derived from the average range, so if the Range chart is out of control, then the control limits on the X-bar chart are meaningless.

After reviewing the Range chart, interpret the points on the X-bar chart relative to the control limits and Run Tests. Never consider the points on the X-bar chart relative to specifications, since the observations from the process vary much more than the subgroup averages.

Interpreting the Range Chart

On the 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 Range, Range control limits, average X-bar and X-bar control limits.

Also on the 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 will have to look at how you measure the variable, and try to measure it more precisely.

Once you have removed the effect of the out of control points from the Range chart, look at the X-bar Chart.

Interpreting the X-bar Chart

After reviewing the Range chart, look for out of control points on the X-bar 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 X-bar and X-bar control limits.

Look for obviously non-random behavior. Turn on the Run Tests, which apply statistical tests for trends to the plotted points.

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:

When to Use an X-bar / R Chart

Tools

Concepts

Interpretation & Calculations

Histograms, Process Capability

Applications

Key Success Factors for the Implementation of SPC

How to Study Process Capability

SPC to Improve Quality, Reduce Cost

Use Of SPC To Detect Process Manipulation