Xbar-R Control Chart
The Xbar-R chart is a SPC Chart control chart for data collected in small subgroups — typically 2 to 10 samples measured together at each point in time. It uses the range within each subgroup to estimate process variability.
Subgrouping is the classic setup for control charting: instead of one reading, you take a handful of measurements close together (five parts off a line every hour, three test specimens per batch) and treat them as one rational subgroup. The spread within a subgroup captures the natural short-term variation of the process, and the Xbar-R chart uses it to judge whether the process level and spread are stable.
The subgroup size must be between 2 and 25; Xbar-R is at its best for subgroups of roughly 10 or fewer, where the range is an efficient measure of spread.
Select X-bar (Xbar-R) for the subgroup-means chart or R (Xbar-R) for the range chart in the Chart Type dropdown.
How It Works
Xbar-R 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. Its control limits are derived from the average range across subgroups, so the range chart's estimate of variability sets the width of the means chart.
R Chart
The R chart plots the range (maximum − minimum) of each subgroup, monitoring the within-subgroup variability. Check the R chart first: if the spread is unstable, the control limits on the X-bar chart are not trustworthy, because they are built from the average range.
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.
For subgroups larger than about 10, the range becomes a less efficient estimator of spread than the standard deviation — prefer the Xbar-S chart there.
Methods and Formulas
Let X̅̅ be the grand mean (the mean of all subgroup means) and R̅ the average range across subgroups.
| Chart | Center line | UCL | LCL |
|---|---|---|---|
| X-bar | X̅̅ | X̅̅ + A2 × R̅ | X̅̅ − A2 × R̅ |
| R | R̅ | D4 × R̅ | D3 × R̅ |
A2, D3, and D4 are standard SPC constants that depend on the subgroup size, tabulated for sizes 2 through 25. For subgroup sizes of 6 or fewer, D3 = 0 and the R chart's lower limit is 0.
When to Use It
| Scenario | Chart |
|---|---|
| Small subgroups (2–10 samples) | Xbar-R |
| Larger subgroups (10+ samples) | Xbar-S |
| 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 R charts of a pair report identical numbers. Like every chart type, Xbar-R works with both a time and a numeric X-axis.
The Xbar-R chart is part of SPC Chart. See the main documentation for control lines, the statistics table, capability indices, and CSV export.