Xbar-S chart

An Xbar-S chart plots the process mean (Xbar chart) and process standard deviation (S chart) over time for variables data in subgroups. This combination control chart is widely used to examine the stability of processes in many industries.

For example, you can use Xbar-S charts to examine the process mean and variation for subgroups of part lengths, call times, or hospital patients' blood pressure over time.

The Xbar chart and the S chart are displayed together because you should interpret both charts to determine whether your process is stable. Examine the S chart first because the process variation must be in control to correctly interpret the Xbar chart. The control limits of the Xbar chart are calculated considering both process spread and center. If the S chart is out of control, then the control limits on the Xbar chart may be inaccurate and may falsely indicate an out-of-control condition or fail to detect one.

Use the Xbar-S chart when your subgroup size is 9 or more. You can use the Xbar-R chart when your subgroup size is 8 or less.

Example:

A paint manufacturer wants to assess the stability of the process used to fill paint cans. Analysts collect subgroups of 10 cans every hour and use an Xbar-S chart to monitor the mean and variation of the filled paint cans.

Xbar S chart

The points vary randomly around the center line and are within the control limits. No trends or patterns are present. The variability in the fill weight is stable across the 30 subgroups.