Calculator Input
Paste a balanced crossed study with columns: Part, Operator, Trial, Value.
Example Data Table
This balanced example uses 3 parts, 2 operators, and 3 trials per part.
| Part | Operator | Trial | Value |
|---|---|---|---|
| P1 | A | 1 | 10.02 |
| P1 | A | 2 | 10.00 |
| P1 | A | 3 | 10.01 |
| P1 | B | 1 | 10.05 |
| P1 | B | 2 | 10.03 |
| P1 | B | 3 | 10.04 |
| P2 | A | 1 | 10.30 |
| P2 | A | 2 | 10.29 |
| P2 | A | 3 | 10.31 |
| P2 | B | 1 | 10.34 |
| P2 | B | 2 | 10.33 |
| P2 | B | 3 | 10.35 |
Formula Used
1. Equipment Variation (EV): EV = R̄ / d2(r)
R̄ is the average within-cell range. d2(r) depends on trial count.
2. Appraiser Variation (AV): AV = √[(Rop / d2(o))² − EV² / (p × r)]
Rop is the range of operator means. Negative values are set to zero.
3. Part Variation (PV): PV = Rpart / d2(p)
Rpart is the range of part means across all parts.
4. Total Gage R&R: GRR = √(EV² + AV²)
5. Total Variation: TV = √(GRR² + PV²)
6. Number of Distinct Categories: ndc = floor(1.41 × PV / GRR)
Percent study variation uses 6σ values. Percent tolerance uses (6σ ÷ tolerance) × 100 when tolerance is supplied.
How to Use This Calculator
- Collect a balanced crossed study with repeated measurements.
- Use consistent part names, operator labels, and trial numbers.
- Paste the study into the measurement box as CSV rows.
- Enter tolerance width, or provide LSL and USL values.
- Click the calculate button to generate the summary table.
- Review total Gage R&R, ndc, and tolerance percentages.
- Use the CSV or PDF buttons to save the report.
Interpretation Guide
Below 10% study variation: usually acceptable for most decisions.
10% to 30%: conditionally usable depending on product risk, cost, and process controls.
Above 30%: improvement is normally required before relying on the system.
ndc of 5 or more: generally indicates useful part discrimination.
Frequently Asked Questions
1. What does Gage R&R measure?
It estimates how much observed variation comes from the measuring system instead of true part differences. It separates repeatability and appraiser effects.
2. Why must the study be balanced?
Balanced data ensures every part is measured by every operator across the same trial count. That structure supports stable crossed-study calculations.
3. What is repeatability?
Repeatability is short-term equipment variation. It reflects how much readings change when the same operator measures the same part repeatedly.
4. What is reproducibility?
Reproducibility is appraiser-to-appraiser variation. It shows whether different operators obtain systematically different average results on the same parts.
5. What does ndc mean?
The number of distinct categories estimates how many part groups the system can reliably separate. Larger values mean better discrimination power.
6. How is tolerance percentage used?
It compares six-sigma measurement spread to allowed specification width. Lower percentages show the measurement system consumes less of the tolerance band.
7. When is a result considered acceptable?
A common rule treats below 10% as acceptable, 10% to 30% as marginal, and above 30% as needing improvement.
8. Can I use this for destructive testing?
Not usually. Destructive tests often require alternative study designs because repeated trials on the same physical part may not be possible.