Interpreting an X-bar / S Chart

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

Interpreting the Sigma Chart

On the Sigma 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 Sigma, Sigma control limits, average X-bar and X-bar control limits. (This can be done automatically using the Auto Drop feature in our SPC software).

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

Interpreting the X-bar Chart

After reviewing the Sigma 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.