Control limits
The simplest rule suggesting a special cause is any value that is outside two control limits. The values 2000 ml and 2080 ml on the run chart in the previous page might be used as control limits. More extreme values in the process suggest that it is out of control — they trigger an examination of the process for a special cause.
Since control limits on a run chart are used to trigger an examination of the production process — possibly a costly exercise — we must set them wide enough that they are rarely exceeded when the process is stable.
Accuracy of the 70-95-100 rule of thumb
The 70-95-100 rule of thumb implies that values should rarely be more than 3 standard deviations from the mean if the process is in control.
Although the actual proportion of values outside the mean ± 3 st devn control limits depends on the shape of the distribution, it is a rare occurrence for all distributions when the process is under control. However:
Control limits at ± 3 standard deviations from the process mean should be avoided for very skew distributions.
If the measurements are very skew, consider transforming the data before producing a run chart.