Gage R&R calculation walkthrough

Learning objectives

• Structure a 10×3×2 crossed continuous Gage R&R study.
• Separate repeatability, reproducibility and part-to-part variation.
• Interpret %Study Variation and %Tolerance correctly.

Core idea

Crossed continuous Gage R&R partitions measurement variance into equipment (repeatability) and appraiser (reproducibility) parts and compares them to part-to-part variation and to tolerance.

Spreadsheet lab

• Layout: 10 parts × 3 inspectors × 2 blind randomized trials.
• Compute part means, inspector means, cell means.
• Repeatability σ from within-cell variation; reproducibility σ from inspector effect; part-to-part σ from part effect (all via mean squares).
• %Study = 100 × σ_MS / σ_total; %Tolerance = 100 × 6σ_MS / (USL−LSL).

Garment-factory example

Chest measurement on 10 polos by 3 inspectors, 2 trials each: σ_repeatability = 0.18 cm, σ_reproducibility = 0.12 cm, tolerance = 2 cm → %Tolerance ≈ 100 × 6 × 0.22 / 2 = 64.9% — measurement dominates; retrain and refix jig before capability.

Method

1. Select parts spanning the process range.
2. Randomize and blind the trials.
3. Compute variance components, %Study and %Tolerance.
4. Improve the system if %Tolerance > 30% before drawing product conclusions.

Common mistakes

• Using only one inspector — no reproducibility captured.
• Choosing easy parts that hide part-to-part variation.
• Reporting %Study without %Tolerance for spec-driven decisions.