Gauge R&R Calculator

Formula

• X̄-R: σ_EV = R̄ / d2(r); EV = K · σ_EV (K = 6 default, or 5.15 legacy).
• σ_AV² = max(0, (X̄diff / d2(k))² − σ_EV² / (n · r)); AV = K · σ_AV.
• σ_PV = Rp / d2(n); PV = K · σ_PV.
• GRR = √(EV² + AV²); TV = √(GRR² + PV²).
• %GRR (tolerance) = GRR / Tol × 100; %GRR (study) = GRR / TV × 100.
• NDC = floor(1.41 × PV / GRR). AIAG gates: <10% acceptable, 10–30% marginal (includes 10%), >30% unacceptable.

How it works

Enter Xbar-R MSA worksheet summaries (R-bar, operator mean range, part mean range) or paste EV/AV/PV components. The pad returns GRR, %GRR against both tolerance and study variation, component shares, NDC, and AIAG Acceptable / Marginal / Unacceptable gates. Sigma multiplier defaults to 6 (AIAG 4th ed.); 5.15 remains available for legacy 99% studies.

Choose Entry mode (X̄-R study summary or EV/AV/PV components). On X̄-R, pick Sigma multiplier K (6 or 5.15) — K is hidden in component mode because EV/AV/PV are already study-variation widths. Enter worksheet summaries or components plus tolerance (USL − LSL). CALCULATE fills Results (variation stack, dual %GRR, NDC, AIAG status). Editing a field clears Results. RESET restores X̄-R defaults with K = 6.

EV, AV, and why %GRR has two denominators

Default CALCULATE path: GRR ≈ 0.094 inside TV ≈ 0.496 → study %GRR ≈ 19%.

Component mode example: EV=AV=0.01, PV=0.05, Tol=0.20 → GRR≈0.01414, study %GRR≈27%, NDC=4 (floor; rounded GRR 0.0141 yields NDC=5).

AIAG gates and NDC

Default study: tolerance gate green, study-variation gate amber, NDC 7.

Sigma multiplier K defaults to 6 (AIAG 4th ed.); choose 5.15 only when your customer still requires the older 99% study width.

X̄-R summary vs ANOVA and attribute MSA

Standard study shape: 10 parts × 3 operators × 2–3 trials, parts spanning the process range, randomized and blinded where practical.

d2 constants use the common Shewhart (g→∞) table keyed by trials, operators, and parts.

Worked example

Default X̄-R summary with K = 6 and tolerance = 1.

1. σ_EV = 0.012 / 1.128 ≈ 0.01064 → EV ≈ 0.0638
2. AV ≈ 0.0694 after operator-range correction; GRR ≈ 0.0943
3. PV ≈ 0.487 → TV ≈ 0.496; NDC = floor(1.41 × PV/GRR) = 7
4. %GRR tol ≈ 9.4% (Acceptable); %GRR study ≈ 19% (Marginal)

Result: Tolerance gate passes; study-variation gate is marginal — tighten the gage before heavy SPC use.

When to use

• Validating a gage before capability studies or control charts
• Turning an MSA worksheet summary into %GRR, NDC, and AIAG status
• Comparing tolerance-based vs study-variation %GRR for the same data
• Quick EV/AV/PV what-if checks when components are already known

Limitations

• X̄-R summary or EV/AV/PV only — not ANOVA from raw measurement tables
• Not for attribute / pass-fail gages (use attribute agreement analysis)
• Not nested/destructive MSA or linearity & bias studies
• d2 uses Shewhart g→∞ values; finite-g d2* tables can differ slightly
• AIAG % gates are guidelines — follow your customer or quality manual

FAQ

What %GRR is acceptable?

AIAG-style guidance: under 10% acceptable, 10–30% marginal, over 30% unacceptable. Always state whether the percentage is vs tolerance or vs study variation — they often differ.

Why do %GRR (tolerance) and %GRR (study) disagree?

Tolerance % uses the specification width; study % uses the observed total variation in the study. A tight process inside a wide tolerance can look good on tolerance % and marginal on study % (or the reverse).

What is NDC?

Number of distinct categories — how many groups the gage can reliably distinguish within the part variation. NDC ≥ 5 is the usual minimum for process control; ≥ 10 is excellent.

Should I use K = 6 or 5.15?

AIAG MSA 4th Edition commonly uses 6 (~99.73% coverage). 5.15 is the older ~99% study width still required by some customers. Pick the K your procedure specifies and keep it consistent across reports.