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X-bar and R control chart template
An X-bar and R control chart follows a process over time with two charts: the mean of each small subgroup of parts (x̄) and the range within it (R). Control limits worked out from the process's own data show how much it varies when nothing unusual is happening, so a point outside them, or a pattern such as a long run on one side of the center line, signals a special cause to find and fix. A control chart answers whether the process is stable; a capability study (Cpk) answers whether a stable process fits the specification. Page 1 of the PDF has the header fields, a data table for 25 subgroups of up to 5 readings with the sum, mean and range, and an x̄ chart and an R chart lined up under the subgroups, each with lines for the center line and the control limits. Page 2 has the limit formulas with the A2, D3, D4 and d2 constants for subgroups of 2 to 10, the common rules for spotting a special cause, a worked example and a reaction log. The Excel version takes subgroups of 2 to 10, works out x̄, R, the grand mean, the average range and both sets of limits, flags points outside the limits and 7 means in a row on one side of the center line, draws both charts with their limits, and has a worked example sheet and a reaction log.
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When to use it
When to use an X-bar and R chart
- For a measured characteristic made in volume, where you can take small subgroups of parts made one after another (2 to 10, most often 4 or 5).
- On the key characteristics in a control plan, to watch the process while it runs instead of sorting parts afterwards.
- Before a capability study, to show the process is stable: a Cpk from an unstable process predicts nothing.
- After a change to a machine, tool, material or method, to see whether the process has shifted.
- Not for one reading at a time (an individuals chart fits better) or for counts of defects (use a p or c chart).
How to fill it in
- 1
Check the gauge first
Run a gauge R&R on the measurement system, so the chart shows the process and not the gauge.
- 2
Choose the subgroup
Parts made one after another, the same number each time, at a set interval: for example 5 parts every hour. Write the readings and the time.
- 3
Work out x̄ and R
For each subgroup, the mean (sum ÷ n) and the range (largest − smallest). Plot both.
- 4
Set the limits
After about 25 subgroups: x̿ ± A₂R̄ for the x̄ chart, D₄R̄ and D₃R̄ for the R chart, with the constants for your subgroup size.
- 5
React to signals
A point beyond a limit, a run of 7 on one side of the center line or a clear trend: find the cause, act on it and write both in the reaction log.
- 6
Keep the limits
Use the same limits on later sheets. Recalculate only after a deliberate process change, or after removing subgroups whose cause you found and fixed.
Constants
Control chart constants by subgroup size
A₂ sets the x̄ chart limits, D₃ and D₄ the R chart limits, and d₂ turns the average range into an estimate of the process standard deviation (R̄ ÷ d₂).
| Subgroup size n | A₂ | D₃ | D₄ | d₂ |
|---|---|---|---|---|
| 2 | 1.880 | 0 | 3.267 | 1.128 |
| 3 | 1.023 | 0 | 2.574 | 1.693 |
| 4 | 0.729 | 0 | 2.282 | 2.059 |
| 5 | 0.577 | 0 | 2.114 | 2.326 |
| 6 | 0.483 | 0 | 2.004 | 2.534 |
| 7 | 0.419 | 0.076 | 1.924 | 2.704 |
| 8 | 0.373 | 0.136 | 1.864 | 2.847 |
| 9 | 0.337 | 0.184 | 1.816 | 2.970 |
| 10 | 0.308 | 0.223 | 1.777 | 3.078 |
2
- A₂
- 1.880
- D₃
- 0
- D₄
- 3.267
- d₂
- 1.128
3
- A₂
- 1.023
- D₃
- 0
- D₄
- 2.574
- d₂
- 1.693
4
- A₂
- 0.729
- D₃
- 0
- D₄
- 2.282
- d₂
- 2.059
5
- A₂
- 0.577
- D₃
- 0
- D₄
- 2.114
- d₂
- 2.326
6
- A₂
- 0.483
- D₃
- 0
- D₄
- 2.004
- d₂
- 2.534
7
- A₂
- 0.419
- D₃
- 0.076
- D₄
- 1.924
- d₂
- 2.704
8
- A₂
- 0.373
- D₃
- 0.136
- D₄
- 1.864
- d₂
- 2.847
9
- A₂
- 0.337
- D₃
- 0.184
- D₄
- 1.816
- d₂
- 2.970
10
- A₂
- 0.308
- D₃
- 0.223
- D₄
- 1.777
- d₂
- 3.078
A filled-in example
Illustrative, not a benchmarkAn example: the bore of a machined housing, specification 24.980 to 25.040 mm, 25 subgroups of 5 (illustrative numbers). The Excel version's Example sheet has the same readings.
- Grand mean x̿ = 25.0104 mm, average range R̄ = 0.01356 mm.
- x̄ chart: A₂ × R̄ = 0.577 × 0.01356 = 0.00782, so UCL = 25.0182 mm and LCL = 25.0026 mm.
- R chart: UCL = 2.114 × 0.01356 = 0.0287 mm, LCL = 0.
- Subgroup 18 has a mean of 25.0254 mm, above the UCL, although every part in it was inside the specification. The tool offset had been entered wrong after an insert change.
The chart caught the shift before any part went out of specification. The offset was corrected and logged, and with subgroup 18 removed the limits became 25.0020 to 25.0176 mm around a grand mean of 25.0098 mm.
Common mistakes
Using the specification as control limits
Specification limits say what the customer allows for one part; control limits say what the process does. Drawing the tolerance on an x̄ chart hides real signals.
Recalculating the limits on every sheet
Limits that move with the data absorb every shift. Set them once from a stable period and keep them.
Charting without reacting
A chart nobody acts on is paperwork. Every signal needs a cause found and a line in the reaction log.
Mixing streams in one subgroup
Parts from two cavities, spindles or machines in one subgroup inflate the range and hide the difference between them. Chart each stream on its own.
Download the template
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Run this template in LeanSuite
In LeanSuite quality checks run as digital checklists with number limits, an out-of-spec answer can raise a tag or start a CAPA automatically, and KPI Builder tracks quality KPIs against targets.
In the lean glossary
FAQ
X-bar and R control chart template: common questions
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