Xbar-s Control Chart: Variable Control for Large Subgroups
What is an Xbar-s Chart?
The Xbar-s chart combines a mean chart (Xbar) and a standard deviation chart (s): the Xbar chart monitors subgroup mean location and the s chart monitors within-subgroup spread using each subgroup's standard deviation. Larger subgroups make the standard deviation a more stable estimator of spread than the range.
When to Use It
Use it for variable data with 8 or more samples per subgroup (10+ is often preferred). Subgroups of 2-8 use Xbar-R for simplicity, and single values use I-MR. Automated inspection and high-volume data collection are typical Xbar-s settings.
How to Read It
Read the s chart first: an out-of-control standard deviation means within-subgroup variation is unstable - investigate measurement-system and dispersion factors. Once the s chart is in control, read the Xbar chart: an out-of-control mean signals a center shift. The tool flags anomalies automatically using the eight run rules.
Control Limits
Xbar chart: UCL/LCL = Xbar +/- A3*sbar. s chart: UCL = B4*sbar and LCL = B3*sbar (for small subgroups B3 can be 0, so the s chart has no lower limit). A3, B3 and B4 are constants that depend on subgroup size; the tool looks them up automatically.