I-MR-R/S (Between/Within) Chart
The I-MR-R/S, or Between/Within, chart set is a SPC Chart PRO tool for subgrouped data that varies both between subgroups and within them — the situation an ordinary Xbar-R or Xbar-S chart gets wrong.
An Xbar chart assumes the only reason subgroup means differ is the variation within the subgroups. In many real processes that is not true: each batch, lot, or run has its own level, and those levels drift from one to the next by more than the within-subgroup spread would predict. When that between-subgroup component is present, Xbar limits — built from within-subgroup variation alone — are far too tight, and almost every subgroup looks out of control even though nothing is wrong. The Between/Within charts widen the limits on the subgroup means to include the between-subgroup variation, so they flag only genuine signals.
When to Use It
Reach for Between/Within when your data is collected in subgroups and the subgroups are natural groupings that carry their own level — batches from a reactor, cavities in a mold, wafers from a run, parts from one setup. The tell-tale sign is an Xbar-R chart on which nearly every point is out of control: that usually means a between-subgroup component the Xbar chart isn't accounting for, not a process in chaos.
If the subgroups are just convenient samples of one stable stream, a plain Xbar-R or Xbar-S chart is the right tool.
The Three Charts
Between/Within is a set of three charts, each a separate Chart type you add as its own panel — all sharing the same query and subgroup size. Minitab stacks them in one window; here you place them side by side.
| Chart type (in the dropdown) | Plots | Watches |
|---|---|---|
| I chart (I-MR-R/S between/within) | The subgroup means, as individuals | The process level over time, with limits that include the between-subgroup variation |
| MR chart (I-MR-R/S between/within) | The moving range of the subgroup means | The between-subgroup variation itself — is the batch-to-batch shift stable? |
| R chart / S chart (I-MR-R/S between/within) | The within-subgroup range (R) or standard deviation (S) | The within-subgroup spread — is the variation inside each subgroup stable? |
The I chart is the headline: its limits come from the moving range of the means (the between-subgroup variation), so genuine batch-to-batch drift stays in control while a real level shift still stands out. The MR chart confirms the between-subgroup variation is stable, and the R or S chart confirms the within-subgroup variation is stable — a spike there (as in the image above) flags a subgroup that fanned out internally.
Setting It Up
- Add a panel for each chart you want — typically the I, MR, and one of R / S.
- Point all of them at the same query and set the same Subgroup size in the SPC section. Each consecutive block of that many rows is one subgroup.
- Choose R for small subgroups and S for larger ones — the range is simple and effective up to about 8–10 per subgroup, while the standard deviation uses all the data and is preferred beyond that.
Methods and Formulas
Let X̄ be the grand mean of the subgroup means, MR̄ the average moving range of the subgroup means, R̄ and S̄ the average within-subgroup range and standard deviation, and n the subgroup size.
| Chart | Center line | Control limits |
|---|---|---|
| I (of the means) | X̄ | X̄ ± 2.66·MR̄ |
| MR (of the means) | MR̄ | D4·MR̄ and D3·MR̄ (n = 2 constants) |
| R (within) | R̄ | D4·R̄ and D3·R̄ |
| S (within) | S̄ | B4·S̄ and B3·S̄ |
The I chart's limits use the moving range of the means — the same 2.66 (= 3 ⁄ d2) constant as an I-MR chart, applied to the subgroup means — which is exactly how the between-subgroup variation enters. The R and S charts are the same within-subgroup range and standard-deviation charts as in Xbar-R and Xbar-S.
Capability
For capability (Cp/Cpk), the panel estimates the total standard deviation of the individual measurements by combining both components:
σtotal = √( Smr2 + σwithin2·(1 − 1 ⁄ n) )
where Smr = MR̄ ⁄ d2 is the standard deviation of the subgroup means (the between-subgroup component) and σwithin = S̄ ⁄ c4 is the within-subgroup standard deviation. This between/within estimate applies on any panel of the set. As always, capability needs specification limits.
Between/Within charts take their data in the same shape as any subgrouped chart — one measurement per row, grouped by the Subgroup size. The subgroup size and chart type are saved with the dashboard, and every chart works with both a time and a numeric X-axis.
I-MR-R/S is part of SPC Chart PRO. For requirements, licensing, and support, see the SPC Chart PRO documentation.