Samples instead of individual values

Although control charts for individual values are sometimes used, it is more common to examine samples from a process at regular intervals rather than individual values.

Control chart for means

This avoids the problem that the 70-95-100 rule of thumb is poor for skew distributions — sample means have distributions that are closer to normal than individual values. If the sample size is n,

 = 

The control limits for a control chart of sample means are therefore...

 ±  3

where and s are estimates of the mean and standard deviation of individual values when the process is in control. These control limits should be distinguished carefully from the corresponding control limits for individual values,

 ±  3s

Since the control limits used in a control chart for means are closer to than those in a control chart for individual values, the chart is more sensitive to changes in the process mean over time.

Training data

In the example below, the control limits use the mean, , and standard deviation, s, from a training period of five samples to set control limits for individual values.

where