Xbar-S Control Chart
The Xbar-S chart is a SPC Chart control chart for data collected in subgroups, using the standard deviation within each subgroup to estimate process variability. It is the counterpart to the Xbar-R chart and is generally preferred for larger subgroups — typically more than 10 samples — where the range becomes a less efficient estimator of spread.
The idea is the same as Xbar-R: take several measurements together as a rational subgroup and use the variation within each subgroup to set the control limits. The difference is that Xbar-S summarizes each subgroup's spread with its standard deviation, which uses every value in the subgroup rather than just the two extremes — a more efficient and stable estimate as the subgroup grows.
The subgroup size must be between 2 and 25.
Select X-bar (Xbar-S) for the subgroup-means chart or S (Xbar-S) for the standard-deviation chart in the Chart Type dropdown.
How It Works
Xbar-S is a pair of charts read together — one for the process level, one for its within-subgroup spread:
X-bar Chart
The X-bar chart plots the mean of each subgroup in sequence, monitoring the central tendency of the process — identical in purpose to the X-bar chart of an Xbar-R pair. Here, though, the control limits are based on the average standard deviation rather than the average range.
S Chart
The S chart plots the sample standard deviation of each subgroup, monitoring the within-subgroup variability. As with Xbar-R, read the spread chart first: if the S chart is out of control, the X-bar limits built from the average standard deviation cannot be trusted.
Subgroup Size
Set the Subgroup size (2–25) in the SPC section. Consecutive rows are grouped into subgroups of that size, and each subgroup contributes one plotted point to each chart. The size can also be driven by the subgroupSize dashboard variable.
The subgroup standard deviation uses Bessel's correction (dividing by n − 1). For small subgroups either Xbar-S or Xbar-R works; the advantage of Xbar-S grows with the subgroup size.
Methods and Formulas
Let X̅̅ be the grand mean (the mean of all subgroup means) and S̅ the average sample standard deviation across subgroups.
| Chart | Center line | UCL | LCL |
|---|---|---|---|
| X-bar | X̅̅ | X̅̅ + A3 × S̅ | X̅̅ − A3 × S̅ |
| S | S̅ | B4 × S̅ | B3 × S̅ |
A3, B3, and B4 are standard SPC constants that depend on the subgroup size, tabulated for sizes 2 through 25. For smaller subgroups B3 = 0 and the S chart's lower limit is 0.
When to Use It
| Scenario | Chart |
|---|---|
| Larger subgroups (10+ samples) | Xbar-S |
| Standard deviation is the better variability estimate | Xbar-S |
| Small subgroups (2–10 samples) | Xbar-R |
| Individual measurements, no subgroups | XmR |
The chart type and subgroup size are saved with the dashboard. The descriptive statistics and capability indices in the statistics table always describe the raw individual measurements, so the X-bar and S charts of a pair report identical numbers. Like every chart type, Xbar-S works with both a time and a numeric X-axis.
The Xbar-S chart is part of SPC Chart. See the main documentation for control lines, the statistics table, capability indices, and CSV export.