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: $\%GRR = \frac{\sigma_{GRR}}{\sigma_{total}} \times 100\%$ or $\%GRR_{tolerance} = \frac{6\sigma_{GRR}}{Tolerance} \times 100\%$.
• ndc: Number of Distinct Categories — $ndc = 1.41 \times \frac{\sigma_{parts}}{\sigma_{GRR}}$ — 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.