ndc 19 | Acceptable
Separate part variation from measurement variation.
Before you trust any process data, ask how much of the observed variation is the process. Then ask how much of it is the measurement system itself. If the gage cannot discriminate between parts, every capability number computed from it is fiction.
A Gage R&R study divides the total measurement variation into three parts. Part-to-part variation is the variation you want to see. Repeatability is the variation of one operator who measures the same part again. Reproducibility is the difference between operators. The ANOVA method also tests for a part-by-operator interaction. An interaction shows that some operators measure certain parts differently.
One measurement system passes. One fails for a clear reason.
ndc 2 | Unacceptable
| Metric | PASS case | FAIL case |
|---|---|---|
| %GRR, study variation | 7.16% | 43.55% |
| ndc | 19 | 2 |
| Verdict | Acceptable | Unacceptable |
| Primary cause | Measurement system acceptable | Reproducibility, 95.9% of GRR |
The failing gage drags apparent Cpk to the acceptance boundary.
1.5000
True process Cpk
1.3337
Measured through FAIL gage
At canonical seed 20260723, the observed result lands at the 1.33 boundary, not below it. The reviewed population expectation from the injected components is 1.2815, or about 1.28. The observed Cpk loss is 11.08%.
| Scenario | Apparent total sd (mm) | Apparent Cpk | Cpk loss |
|---|---|---|---|
| True process (no measurement error) | 1.0000 | 1.5000 | 0.00% |
| Measured through the PASS gage | 1.0096 | 1.4857 | 0.95% |
| Measured through the FAIL gage | 1.1247 | 1.3337 | 11.08% |
The same diagnostic views for both systems.
Each chart is embedded directly from the generated PNG artifact.
PASS case
Acceptable
FAIL case
Unacceptable
A point estimate is not a confidence bound.
With 3 operators, reproducibility is estimated with only 2 degrees of freedom. A single study cannot pin %GRR precisely, even when the verdict remains robust for a clearly failing case.
48%Mean %GRR
48%Median %GRR
18 percentage pointsStandard deviation
17.8% to 77.5%5th to 95th percentile
The point estimate can swing about 20 percentage points from run to run. The canonical FAIL verdict is still robust because the designed case is far from the marginal band.
A crossed ANOVA study.
Study design
| Parameter | Value |
|---|---|
| Design | Crossed (every operator measures every part) |
| Parts | 10, spanning the process range (part sd = 1.0 mm) |
| Operators | 3 |
| Replicates | 3 per operator per part |
| Total measurements | 90 |
| Method | ANOVA with part-by-operator interaction |
| Interaction test | F-test at alpha = 0.25 (AIAG convention) |
Decision thresholds
| %GRR, study variation | Verdict |
|---|---|
| Under 10% | Acceptable |
| 10% to 30% | Marginal |
| Over 30% | Unacceptable |
Every dataset, number, chart, and test result on this page is generated from the frozen plan and the canonical seed.
This validates the method, not a physical gage.
- Simulated primary data: This validates the method against known truth. It is not a substitute for a real gage study on physical hardware.
- Crossed design only: Every operator measures every part (non-destructive). Nested or destructive designs require a different ANOVA structure and are out of scope.
- No time-dependent effects: The simulation does not capture day-to-day or setup-to-setup variation, which in real studies can exceed short-term repeatability.
- The two cases are deliberately unambiguous: Both sit far from the 10-30% marginal band. The method therefore shows clearly. This is a teaching demonstration, not a claim about a specific real gage. Real gages often fall in the marginal band where the decision depends on application context.