This worked example uses the same 20 measurements loaded by the Mechatrovich MSA preview. Every operator measures every part twice, making it a crossed Gage R&R study. It demonstrates the calculation; a formal study must follow the approved sampling, randomization, method, and reporting requirements for the application.
1. Study setup and measurements
Five parts span approximately 10.02 to 10.54 mm. Operators A and B each measure every part twice with the same method.
| Part | A · T1 | A · T2 | B · T1 | B · T2 | Part mean |
|---|---|---|---|---|---|
| 1 | 10.018 | 10.021 | 10.024 | 10.020 | 10.02075 |
| 2 | 10.146 | 10.150 | 10.153 | 10.149 | 10.14950 |
| 3 | 10.278 | 10.274 | 10.281 | 10.276 | 10.27725 |
| 4 | 10.407 | 10.412 | 10.415 | 10.410 | 10.41100 |
| 5 | 10.536 | 10.532 | 10.541 | 10.537 | 10.53650 |
The part means are deliberately separated, creating a strong part-to-part signal.
2. Calculate repeatability
For every operator and part, calculate the range between the two repeated readings. The average of the ten ranges is 0.00420 mm.
Equipment Variation (EV) = R̄ × 4.56 = 0.019152 mmEV represents variation when the same operator measures the same part repeatedly under the study conditions.
3. Calculate reproducibility
The overall operator means are 10.2774 mm for A and 10.2806 mm for B—a difference of 0.0032 mm. After correcting this operator component for repeatability:
Appraiser Variation (AV) = 0.009987 mmAV is smaller than EV, so repeated readings contribute more variation than the operator-average difference in this dataset.
4. Combine the measurement components
Total Gage R&R = √(EV² + AV²) = 0.021600 mmThis combined measurement variation must be compared with part-to-part and total variation.
5. Calculate part and total variation
Part Variation (PV) = 1.139808 mm
Total Variation (TV) = √(GRR² + PV²) = 1.140012 mmPV is much larger than GRR because the chosen parts span a broad range while repeated readings remain close.
6. Review the outputs
| Output | Result | Meaning |
|---|---|---|
| Repeatability / study variation | 1.7% | Repeated-measurement contribution |
| Reproducibility / study variation | 0.9% | Operator-average contribution |
| Total GRR / study variation | 1.9% | Combined measurement contribution |
| Part-to-part / study variation | 100.0% | Observed variation is dominated by parts |
| Number of distinct categories | 74 | Strong discrimination in this sample |
7. Interpret more than the status
Total GRR of 1.9% is below the familiar 10% general-guidance band, and ndc is high. For this sample, measurement variation is small relative to the observed part range.
This does not automatically approve the system. Verify that parts represent the actual process range, order was randomized, operators followed the normal method, resolution is adequate, and the calculation matches the required procedure.
Important: %Study Variation depends on part range. Widely separated parts can reduce %GRR and increase ndc. Review %Tolerance when specifications matter, and never choose an artificial part range merely to improve the result.
8. What to investigate next
- Compare repeated ranges for unusual part/operator combinations.
- Observe location, alignment, contact, force, and handling.
- Check resolution, calibration, fixture condition, and environment.
- Review whether the small operator offset points to technique differences.
- Repeat the study after any method improvement.
Reproduce the example
Open the working preview, load the sample study, and calculate. Change individual readings to see how EV, AV, Total GRR, and ndc respond.