gage r&r study

**Gage R&R Study** (Gage Repeatability and Reproducibility) is the **standard MSA experiment that quantifies the total measurement system variation** — determining how much of the observed variation is due to the measurement system (repeatability + reproducibility) versus actual part-to-part differences. **Gage R&R Method** - **Design**: $k$ operators × $n$ parts × $r$ replicates (typical: 3 operators × 10 parts × 3 reps = 90 measurements). - **ANOVA**: Analysis of Variance decomposes total variation into repeatability, reproducibility, and part-to-part components. - **%GRR**: $\%GRR = frac{sigma_{GRR}}{sigma_{total}} imes 100\%$ or $\%GRR_{tolerance} = frac{6sigma_{GRR}}{Tolerance} imes 100\%$. - **ndc**: Number of Distinct Categories — $ndc = 1.41 imes frac{sigma_{parts}}{sigma_{GRR}}$ — should be ≥ 5. **Why It Matters** - **Acceptance Criteria**: %GRR < 10% = excellent; 10-30% = marginal; >30% = unacceptable — the gage needs improvement. - **Decision Making**: High %GRR means measurement noise obscures real process variation — unreliable SPC and capability. - **Required**: IATF 16949 requires Gage R&R for all critical measurements — mandatory for automotive suppliers. **Gage R&R** is **the measurement system exam** — quantifying whether the measurement system contributes acceptable or excessive variation to the total observed variation.