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Gage R&R study sheet
A gage R&R study measures how much of the variation you see comes from the measurement system itself. Repeatability, or equipment variation (EV), is the spread when one appraiser measures the same part several times; reproducibility, or appraiser variation (AV), is the difference between appraisers. Together they make GRR, which is compared with the part-to-part variation (PV) and the total variation (TV). This template uses the average and range method of the AIAG Measurement Systems Analysis (MSA) manual with 10 parts, 2 or 3 appraisers and 2 or 3 trials. Page 1 of the PDF is the data sheet, with the averages and ranges for each appraiser and the part averages. Page 2 has every calculation step with the K1, K2, K3 and D4 constants, a column with the worked example, the %GRR guidance and the number of distinct categories (ndc). The Excel version works out the averages and ranges, the average range, the range limit with any range above it flagged, the difference between appraisers, the range of the part averages, EV, AV, GRR, PV and TV, each as a % of total variation, ndc, an optional % of tolerance and the %GRR band, with an Example sheet that matches the worked example on this page.
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When to use it
When to run a gage R&R study
- Before a capability study or a control chart, so the data shows the process and not the gauge.
- For a new gauge, a gauge moved to a new process, or after a repair that could change how it reads.
- When a customer asks for measurement system analysis in a PPAP, or the control plan names the gauge for a special characteristic.
- When operators disagree about whether parts are good, or parts pass at one station and fail at the next.
How to fill it in
- 1
Choose 10 parts
Parts from normal production that cover the spread of the process, not all from the middle. Number them where the appraisers cannot see.
- 2
Choose the appraisers
Two or three people who use the gauge on the job, with the same gauge and the usual method.
- 3
Measure blind, in random order
Each appraiser measures all 10 parts, then again in a new order for each trial, without seeing the earlier readings.
- 4
Check the ranges
Work out each part's range for each appraiser and the average range. A range above D4 × the average range points to a misread or a damaged part: find out why and re-measure.
- 5
Work out the results
EV from the average range, AV from the difference between appraiser averages, GRR, PV from the range of part averages, then each as a % of total variation, and ndc.
- 6
Decide
Under 10% GRR is generally acceptable, 10% to 30% may be acceptable depending on the application, and over 30% means the measurement system needs fixing. Check ndc too: 5 or more is the usual requirement.
Constants
Average and range method constants
K1 depends on the number of trials, K2 on the number of appraisers, and K3 on the number of parts: 0.3146 for the 10 parts in this template. D4 sets the upper limit for the ranges.
| Constant | With 2 | With 3 |
|---|---|---|
| K1, by trials | 0.8862 | 0.5908 |
| K2, by appraisers | 0.7071 | 0.5231 |
| D4, by trials | 3.267 | 2.574 |
K1, by trials
- With 2
- 0.8862
- With 3
- 0.5908
K2, by appraisers
- With 2
- 0.7071
- With 3
- 0.5231
D4, by trials
- With 2
- 3.267
- With 3
- 2.574
A filled-in example
Illustrative, not a benchmarkAn example: flange thickness, 5.00 ± 0.15 mm, 10 parts, 3 appraisers, 3 trials each (illustrative readings). The Excel version's Example sheet has all 90 readings and gives the same results.
- Average ranges of 0.0058, 0.0074 and 0.0064 mm give an overall average range of 0.00653 mm. The range limit is 2.574 × 0.00653 = 0.0168 mm, and no range is above it.
- EV = 0.00653 × 0.5908 = 0.00386 mm. Appraiser averages are 4.96233, 4.96773 and 4.95870 mm, a difference of 0.00903 mm, so AV = √((0.00903 × 0.5231)² − 0.00386² ÷ 30) = 0.00467 mm.
- GRR = √(0.00386² + 0.00467²) = 0.00606 mm. Part averages run from 4.90767 to 5.02944 mm, a range of 0.1218, so PV = 0.1218 × 0.3146 = 0.0383 mm and TV = 0.0388 mm.
- Of total variation: EV 10.0%, AV 12.0%, GRR 15.6%, PV 98.8%. ndc = 1.41 × 0.0383 ÷ 0.00606 = 8.9, rounded down to 8. GRR is 12.1% of the 0.30 mm tolerance.
15.6% sits in the 10% to 30% band: usable for this characteristic if the customer agrees. AV is larger than EV, which points at how the appraisers measure rather than at the gauge, and appraiser B reads highest on average, so the next step was to agree one way of holding the micrometer and train all three.
Common mistakes
Parts from a narrow band
If the 10 parts are nearly the same, PV is small and %GRR of total variation looks poor even with a good gauge. Pick parts across the process spread.
Appraisers who know which part is which
They remember earlier readings. Hide the numbers and change the order every trial.
Ignoring a range above the limit
One misread inflates EV. Find the cause and re-measure before quoting the result.
Quoting %GRR without saying of what
% of total variation and % of tolerance give different numbers. Say which you report and why.
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Run this template in LeanSuite
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