Learn · updated 2026-10-21
The I-MR chart (individuals and moving range)
Use an I-MR chart when you get one measurement at a time: one reading per batch, per shift or per day. It is two charts: the individual values, and the moving range between neighbouring values.
The formulas. x̄ is the mean of the values, MR̄ the mean of the moving ranges |xᵢ − xᵢ₋₁|.
Individuals chartUCL = x̄ + 2.66 × MR̄CL = x̄LCL = x̄ − 2.66 × MR̄Moving range chartUCL = 3.267 × MR̄CL = MR̄LCL = 0
2.66 is 3 / 1.128 (three sigma, with σ estimated as MR̄ / d2 for ranges of 2). 3.267 is the D4 constant for n = 2.
Worked example: NIST flow rate
Ten batches from the NIST/SEMATECH e-Handbook:
| Batch | Flow rate | Moving range |
|---|---|---|
| 1 | 49.6 | — |
| 2 | 47.6 | 2.0 |
| 3 | 49.9 | 2.3 |
| 4 | 51.3 | 1.4 |
| 5 | 47.8 | 3.5 |
| 6 | 51.2 | 3.4 |
| 7 | 52.6 | 1.4 |
| 8 | 52.4 | 0.2 |
| 9 | 53.6 | 1.2 |
| 10 | 52.1 | 1.5 |
- Mean of the ten values: x̄ = 50.81.
- Mean of the nine moving ranges: MR̄ = 1.8778.
- Individuals limits: 50.81 ± 2.66 × 1.8778 → UCL 55.80, LCL 45.82.
- Moving range limit: 3.267 × 1.8778 = 6.13.
These match the values NIST prints (UCL 55.80, LCL 45.82). LimitLine runs this exact example as a regression test on every release; see the validation page.
Reading it
- A point beyond a limit on either chart is a signal: something changed. Find out what before adjusting anything.
- Patterns inside the limits can also be signals: long runs on one side of the centre line, steady trends. These are the Nelson rules.
- No signals means the variation looks like common cause. Don't react to individual ups and downs; improve the process as a whole if it isn't good enough.
When not to use it
If you measure several parts per sample, an X̄-R or X̄-S chart is more sensitive. If you count defects or defectives, use an attribute chart. See which control chart to use. The I-MR chart also assumes roughly normal data more than the X̄ charts do, so check a histogram.