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Am I measuring the process, or measuring my gauge?

Find out how much of the variation you are looking at is the measurement system rather than the process, by the crossed ANOVA method.

Gage R&R · measure · Yellow Belt · free, no account needed

Use this when

  • Two people measure the same part and get different answers
  • Before trusting a capability study or a control chart built on the same gauge
  • A customer or auditor has asked for an MSA

Gage R&R (crossed ANOVA)

sandbox

Not acceptable — 38.00% %GRR of study variation (standard deviation ratio)

38.00% exceeds 30% — unacceptable. The measurement system needs improvement before the data it produces can support a decision.

AIAG MSA 4th ed., Ch. II §D

Gage R&R · % study var

38.00%

Part-to-part · % study var

92.50%

ndc · min 5

3

Variance components with their contribution to total variance and to total study variation.
SourceVariance% Contributionvariance · sums to 100% Study varstd dev · does NOT sum to 100
Repeatability (equipment variation, EV)0.244899.93%31.50%
Reproducibility: appraiser (AV)0.069742.83%16.81%
Reproducibility: appraiser x part interaction0.041581.69%12.98%
Part-to-part (PV)2.1110985.56%92.50%
Gage R&Rrepeatability + reproducibility0.3562114.44%38.00%

The two percentage columns are not the same quantity. %Contribution is a variance ratio and the partition sums to exactly 100%. %Study var is a standard deviation ratio and does not — the sum of square roots is not the square root of the sum. The identity between them is %StudyVar = 10 × √(%Contribution), so a component at 30% contribution reads 54.8% study variation. Comparing one against the other’s thresholds is the most common misreading of a Gage R&R report.

ndc = 3 (3.43 before truncation) — the number of distinct groups of parts this system can actually tell apart. Below 5, so the system can do little more than sort parts into "high" and "low" — it cannot support process analysis.

Interaction: Appraiser*part interaction F(18,60) = 1.5094, p = 0.1187 <= alpha = 0.25. The interaction was RETAINED: appraisers do not measure all parts the same way. Reproducibility is the appraiser term plus the appraiser*part term.

ndc = 3 (raw 3.43); AIAG MSA 4th ed. Ch. II §D requires at least 5. The system cannot reliably distinguish enough groups of parts to support process analysis.

No tolerance range supplied, so %Tolerance was not computed. When a measurement system is used for product acceptance, %Tolerance — not %StudyVar — is the metric AIAG applies the acceptance bands to.

part, appraiser, trial1, trial2, trial3 — one row per combination. Every appraiser measures every part the same number of times.

10 parts × 3 appraisers × 3 trials

USL − LSL. Supply it for %Tolerance; leave it blank and %Tolerance is simply not reported rather than guessed.

How this is calculated

A random-effects two-factor crossed ANOVA with replication. Expected mean squares give the variance components; the interaction is tested against error and pooled into it when p > 0.25, which is AIAG’s rule. Which path was taken is stated above rather than left implicit.

  • Repeatability (equipment) = MSerror.
  • Reproducibility (appraiser) = appraiser + appraiser×part components.
  • Gage R&R = repeatability + reproducibility.
  • Study variation multiplier: AIAG MSA 4th ed. (2010): 6 sigma, 99.73% of a normal distribution. Minitab default.. It cancels out of %StudyVar and %Contribution and ndc — both are ratios — and scales %Tolerance, the absolute EV/AV/GRR/PV/TV study-variation figures.
  • ndc = 1.41 × (part-variation SD / Gage R&R SD), truncated. The numerator is PART variation, not total: total always exceeds part variation, so substituting it always flatters the gauge.

Source: AIAG, Measurement Systems Analysis 4th ed., Ch. III §B (ANOVA method) and Ch. II §D (ndc); Montgomery, D.C., Introduction to Statistical Quality Control 7e, §8.7.

Saved runs can be attached to a project deliverable as evidence. Both what you entered and what the tool computed are stored, so the result can be checked again later.

How this is calculated

Random-effects two-factor crossed ANOVA with replication. Expected mean squares give the variance components: repeatability = MS error, appraiser and appraiser-by-part from the remaining terms, and the interaction is tested against error and pooled into it when p > 0.25 per AIAG's rule, with the path taken stated rather than left implicit. %Contribution is a variance ratio and sums to exactly 100% across the partition; %StudyVar is a standard deviation ratio and does not, with the exact identity %StudyVar = 10 * sqrt(%Contribution). ndc = 1.41 * (part-variation SD / Gage R&R SD), truncated, using PART variation rather than total. A negative variance estimate floored to zero is disclosed rather than hidden.

Source: AIAG, Measurement Systems Analysis 4th ed., Ch. III Sec. B (ANOVA method) and Ch. II Sec. D (number of distinct categories); Montgomery, D.C., Introduction to Statistical Quality Control 7e, Sec. 8.7.

Learn the method