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.
Control limits from the 70-95-100 rule
We usually base the control limits on the mean and standard deviation of the process when it is in control. The 70-95-100 rule of thumb states that in many distributions,
The rule is illustrated in the diagram below.
By setting the upper and lower control limits to be 3 standard deviations on either side of the process mean, we avoid many 'false alarms' when the process is in control.
The normal distribution below shows the variability of a process with mean 52 and standard deviation 0.5.
Click anywhere on the distribution to display the proportion of values within this distance of the process mean.
Click the checkbox Show Mean and St Devn to replace the horizontal axis with a scale showing distances from the mean as multiples of the standard deviation. Verify the 70-95-100 rule for this distribution.
The 70-95-100 rule is a less reliable guideline for non-normal distributions. Select the option Skew distribution from the pop-up menu beneath the diagram and repeat the exercise.
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.