XmR (I-MR) Control Chart
The XmR chart is a SPC Chart control chart for individual measurements — readings taken one at a time, where grouping them into rational subgroups is impractical. It is also known as the Individuals and Moving Range chart, the I-MR chart, or Shewhart's control chart.
XmR is the right choice for automated or continuous processes where a single reading is recorded at each step: a temperature logged every minute, one measurement per batch, a daily cycle time. Because there is no natural subgroup, the chart estimates process variability from the moving range — the change between consecutive readings — instead of the spread within a subgroup.
The subgroup size is fixed at 1.
Select X (XmR) for the individuals chart or mR (XmR) for the moving-range chart in the Chart Type dropdown.
How It Works
The XmR chart is a pair of charts that are read together — one for the process level, one for its short-term variation:
Individual (X) Chart
The X chart plots each individual measurement in sequence. It monitors the central location of the process, showing whether values stay centered on the process mean. Its control limits are set three sigma out, with sigma estimated from the average moving range.
Moving Range (mR) Chart
The mR chart plots the absolute difference between consecutive measurements, showing the short-term variability of the process. A point on the mR chart is the change from the previous reading, so the first point has no moving range and is left blank.
Read the two together: the mR chart tells you whether the variation is stable, and the X chart whether the level is stable. A special cause often shows on one before the other.
Subgroup Size
XmR is an individuals chart, so the Subgroup size is locked to 1 — each row is one point. If your data arrives in natural groups of two or more, an Xbar-R or Xbar-S chart estimates variability more efficiently.
Methods and Formulas
Let X̅ be the mean of the individual values and mR̅ the mean of the moving ranges.
| Chart | Center line | UCL | LCL |
|---|---|---|---|
| X (individuals) | X̅ | X̅ + 2.66 × mR̅ | X̅ − 2.66 × mR̅ |
| mR (moving range) | mR̅ | 3.267 × mR̅ | 0 |
The 2.66 constant is 3 ⁄ d₂ for a moving range of two (d₂ = 1.128), and 3.267 is the D₄ constant for n = 2. The lower limit of the mR chart is always 0 at n = 2 — a moving range cannot be negative.
When to Use It
| Scenario | Chart |
|---|---|
| Individual measurements, no rational subgroups | XmR |
| Small subgroups (2–10 samples) | Xbar-R |
| Larger subgroups (10+ samples) | Xbar-S |
The chart type and subgroup size are saved with the dashboard. Like every chart type, the XmR chart works with both a time and a numeric X-axis.
The XmR chart is part of SPC Chart. See the main documentation for control lines, the statistics table, capability indices, and CSV export.