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.

Interpreting the Range Chart

On the Range chart, look for out of control points and Run test rule violations. 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. 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. (This can be done automatically using the Auto Drop feature in our SPC software).

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, look at how you measure the variable, and try to measure it more precisely.

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

Interpreting the X-bar Chart

After reviewing the Range chart, interpret the points on the X-bar chart relative to the control limits and Run test rules. 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.

If there are any out of control points on the X-bar Chart, 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. 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. (This can be done automatically using the Auto Drop feature in our SPC software).

If the process shows control relative to the statistical limits and Run Tests for a sufficient period of time, then we can analyze process capability relative to requirements. Process capability is only meaningful when the process is stable, since we cannot predict the outcome of an unstable process.