Samples instead of individual values
Individual values from a process often have skew distributions, making the 3-standard deviation control limits less reliable. However if small samples are taken rather than individual values, the sample means will be closer to normally distributed and have more predictable properties in control charts.
Training data
In order to obtain control limits, we must know the mean and standard deviation of the measurements when the process is 'in control'. These are usually estimated from a set of 'training samples' in which great care is taken to avoid special causes.
The process mean,
is estimated by the mean value from the training samples. We will initially
use the standard deviation of the training sample as our estimate, s,
but will describe a better estimate at the end of this page.
Paint primer thickness
As in control charts for individual values, additional triggers can be used that depend on several successive means. These are defined in the same way as those in control charts for individual values. For example, six successive sample means either increasing or decreasing suggest that there might be a special cause.
Better estimate of s from training samples (advanced)
A different estimate of the process standard deviation, σ, is usually preferred to the overall standard deviation of the values in the training samples.
(An alternative estimate of σ that is occasionally used is
Although this estimate is better when the data have a reasonably symmetric distribution, the earlier estimate is more 'robust' to problems in the training data.)