Interpretation & Calculations
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 causes is detected on the Moving Range Chart, it will also appear on the Individual-X chart, thus making the Moving Range chart somewhat redundant; however, if you are using the run test rules on the Moving Range chart, some value may be evident depending on the process conditions).
Interpreting the Moving Range Chart
On the Moving 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 average Moving Range, Moving Range Chart Calculations, average Individual-X and Individual-X Chart Calculations. (This can be done automatically using the Auto Drop feature in our SPC software).
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, 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 Moving Range chart, look at the Individual-X Chart.
Interpreting the Individual-X Chart
After reviewing the Moving Range chart, interpret the points on the Individual-X chart relative to the control limits and Run test rules If there are any, then the 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 and Individual-X Control Limit Calculations. (This can be done automatically using the Auto Drop feature in our SPC software).
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 Moving Average chart to first define process control. See Choosing a Control Chart for Individuals Data
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.
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).