Your Gage R&R Says the System Is Fine. Run It the Other Way and It Doesn't.

Here is a measurement system study. Ten parts, two operators, two trials each — forty readings, the standard AIAG arrangement.

Analyzed by the average-and-range method, the gage consumes 2.78% of study variation. That is comfortably inside the 10% line: acceptable, no discussion, sign it off.

Analyzed by ANOVA, the same forty numbers give 15.69%. That lands in the band where a measurement system is conditionally acceptable — usable only if you can justify it against the cost of the application, and worth investigating first.

Same data. Same day. Two standard methods, both correctly applied. One of them is missing something.

The study

Nothing about it looks wrong. Repeatability is excellent — the two trials agree to a few thousandths everywhere. Neither operator is obviously the problem.

And here is the fact the whole disagreement turns on:

Operator A, mean of all 20 readings:  10.2700
Operator B, mean of all 20 readings:  10.2700

Identical. Not close — identical to four decimal places.

Why the range method says it is fine

The average-and-range method builds reproducibility from exactly one quantity: the spread of the operator averages. In AIAG notation that is X̄diff, and appraiser variation is

AV = √( (X̄diff × K2)² − EV² / (n × r) )

If the operator averages are the same, X̄diff is zero, so AV is zero, and reproducibility contributes nothing at all. What remains is repeatability, which in this study is genuinely tiny. Hence 2.78%.

The method is not being sloppy. It answered the question it was built to answer — do the operators, on average, read differently? — and the answer is no.

What ANOVA sees

Run the same data through a variance-components model and the split comes out like this:

repeatability     2.13%  of study variation
reproducibility  15.54%
part-to-part     98.76%
total gage R&R   15.69%

Reproducibility is 15.5%, from operators whose averages are identical. That is not a contradiction, and the variance table shows why:

variance, repeatability                 0.0000192
variance, reproducibility               0.0010216
variance, operator × part interaction   0.0010216

The reproducibility variance and the interaction variance are the same number. Every bit of the operator disagreement in this study is interaction. The operator main effect is zero, exactly as the range method reported.

The two appraisers do not disagree on average. They disagree as a function of part size.

Read back down the table with that in mind. On P1 operator B reads 0.068 low. By P5 the gap has closed to almost nothing. By P10 B reads 0.068 high — the same distance, the other way. The bias rotates about the middle of the part range rather than sitting as a constant offset, which is precisely why averaging over the parts cancels it to zero.

What that looks like on a real floor

An interaction of this shape has ordinary physical causes, and none of them are exotic:

A fixture that seats large parts slightly differently from small ones. A dial indicator read at a consistent angle by one operator, where parallax error scales with the pointer's travel. A hand-held micrometer where one person's ratchet technique loads a long part differently from a short one. A gage whose scale error was never checked across its range, only at nominal.

Every one of those produces a measurement system that is fine at the middle of the range and progressively wrong toward its ends. If your parts cluster near nominal, you may never see it. The day a job runs at the edge of the range, your measurements are worst exactly where the tolerance matters most.

Why the verdict changes, and not just the number

The acceptance bands make this concrete. Under 10% of study variation, a measurement system is generally acceptable. Between 10% and 30% it may be acceptable depending on the importance of the application and the cost of improvement. Above 30% it is not.

The range method puts this gage at 2.78% — the first band, where nobody asks a second question. ANOVA puts it at 15.69% — the second band, where the standard expects you to justify the decision rather than record it.

That is the practical difference. Not a number that shifts a little, but a study that moves from approved to approved with an argument you now have to make.

How to see it before you run either method

Plot the operator averages for each part, one line per operator, parts along the x-axis.

If the lines are roughly parallel, the operators differ by a constant and both methods will agree with each other. If the lines converge, diverge or cross, you have interaction — and the average-and-range method cannot see it, no matter how carefully you compute it.

It takes about a minute and it tells you which method you are entitled to trust.

The honest version of the comparison

The average-and-range method is not obsolete and it is not wrong. It was designed to be computed by hand on the floor, it uses tabulated constants precisely so that no one needs a variance-components package, and for a straightforward measurement system with no interaction it lands very close to ANOVA.

It also does one thing ANOVA does not: it is transparent. Anyone can check R̄, X̄diff and the constants on paper. That is worth something in a room where a supplier is disputing your result.

But it can only ever report what it measures, and it does not measure interaction. That is why the AIAG MSA manual moved to ANOVA as the preferred method — not because the arithmetic is better, but because the model is bigger. Interaction, nested designs, and destructive testing are all outside what the range method can express.

The failure mode is specific and worth naming: the two methods disagree exactly when the interaction is orthogonal to the operator main effect. If your operators also differ on average, both methods flag it and you will investigate anyway. It is the study where the averages come out even that quietly passes.

Check it yourself

The table above is real data, and the two numbers in this article are reproducible. Paste it into the free Gage R&R calculator — no account, no sign-up — and you will get 15.69% with the variance components broken out, interaction included.

Then run your last study through it. If your reproducibility comes back much larger than the difference in your operator averages would suggest, you are looking at interaction, and whatever the range method told you about that gage was answering a narrower question than the one you asked.

Gage R&R by ANOVA — crossed and nested — runs on the SVEND study bench, which issues the randomized run sheet, captures readings from the instrument, and judges the completed study. The calculator above runs the same crossed ANOVA on readings you already have.