%GRR: %Tolerance vs %Study Variation Explained

The number on the Gage R&R summary is 9.1%. It’s under ten, so you wrote "acceptable" next to element 8, signed the PPAP cover sheet, and moved the gauge back into the rotation. The submission goes out. A week later the customer SQE replies with one line that stops you: "Is that 9% against tolerance, or against study variation? Please send the tolerance-based %GRR." You open the study file, scroll to the summary table, and realize you genuinely don’t know which denominator the template reported — and that the two numbers, from the exact same data, are not close.

That is the most common and most quietly damaging misread in Measurement Systems Analysis. A single Gage R&R produces two percentages that both get called "%GRR," and they can hand you opposite verdicts on the same gauge. Knowing which one you’re looking at — and which one your customer expects — is the difference between a study that survives scrutiny and a rejected element 8.

Two denominators, one gauge

Gage R&R measures the variation of your measurement system — repeatability (the gauge with one appraiser) plus reproducibility (appraiser to appraiser). That combined GRR is an amount of variation, expressed in measurement units, say micrometers. To turn it into a percentage you have to divide it by something, and AIAG MSA lets you divide by two different things:

• %Tolerance = GRR ÷ tolerance. The denominator is the specification width from the drawing. It answers: how much of my tolerance band does measurement error eat up?
• %Study Variation (%SV) = GRR ÷ total study variation. The denominator is the total variation observed across the parts you sampled. It answers: can this gauge resolve the part-to-part variation of this particular set of parts?

Both use the AIAG bands — below 10% acceptable, 10 to 30% conditional, above 30% unacceptable. Both are legitimate. But they answer different questions, and only one of them is fixed by anything outside your control. The tolerance comes from the customer’s drawing and never moves. The total study variation is set entirely by which parts you happened to grab off the line that morning.

Why the same gauge scores 9% and 20%

Walk it through with numbers. Say the combined GRR works out to 10 µm (the 6-sigma spread) and the characteristic tolerance is a 50 µm band, ±25 µm.

%Tolerance is 10 ÷ 50 = 20%. That’s squarely in the conditional zone — this gauge consumes a fifth of the tolerance, and whether it’s fit for release depends on your customer-specific requirements and a documented justification.

Now the %SV, which depends on the parts. Suppose the sampled parts spanned a very wide range — someone deliberately picked pieces across and even beyond the tolerance to "get a good spread," so the part variation (PV) came out around 110 µm. Total variation is √(GRR² + PV²) = √(10² + 110²) ≈ 111 µm. %SV is 10 ÷ 111 = 9%. Acceptable. Same gauge, same data, but the number you report just dropped from a conditional 20% to a comfortable 9%, purely because the parts were spread wide.

Flip it. Run the identical gauge on a tightly controlled, capable process where the real parts cluster inside 15 µm. Now PV is 15 µm, total variation is √(10² + 15²) ≈ 18 µm, and %SV is 10 ÷ 18 = 55% — unacceptable. The gauge didn’t change. The tolerance didn’t change. The %Tolerance is still 20%. But %SV swung from 9% to 55% on nothing but part selection.

That’s the trap. %SV rewards a wide part spread and punishes a capable process, and neither movement tells you anything new about the gauge’s ability to sort good parts from bad against the spec.

Which number is the right one to report?

It depends on what the gauge is for, and AIAG is clear on the principle.

If the gauge’s job is inspection and release — sorting product to a specification, which is exactly what most PPAP element 8 gauges on the control plan do — the relevant question is how much of the tolerance the measurement error consumes. That’s %Tolerance. It is the defensible headline for a conformance gauge, because it’s anchored to the drawing and immune to how you sampled.

If the gauge is used for process control and improvement — where you care whether it can distinguish one part from the next within the process spread — then %Study Variation (and its companion, ndc, the number of distinct categories, which is also driven by the part spread) is the relevant view.

The failure isn’t computing %SV. The failure is computing %SV, labelling it "%GRR," and letting a customer who lives by %Tolerance assume that’s what they received. A 9% that’s really a 20%-of-tolerance gauge is not a lie, but it is an answer to a question nobody asked — and a competent SQE will ask for the tolerance-based number the moment they see a suspiciously flattering %SV on a release gauge.

The objection: "our part sample followed AIAG"

A fair pushback: AIAG says the study parts should represent the full range of process variation, so a wide spread is correct, not gaming. True — for a study aimed at process capability. But representing process variation and demonstrating fitness against tolerance are two different goals, and the honest move is to report both numbers and name each one, not to let the more flattering denominator stand in for the other. When the characteristic is a customer conformance requirement, %Tolerance is the number that decides fitness, and it should be stated as such.

Where PrüfDesk fits — and where it doesn’t

Be precise about this: PrüfDesk does not compute your Gage R&R. The statistics belong to your metrology team and the AIAG method. What PrüfDesk does is guarantee the two facts that make whatever number you report defensible.

First, it holds the specification and tolerance on the instrument and characteristic record — the fixed denominator behind %Tolerance. When the study is built on the drawing-controlled tolerance rather than a value someone retyped into a spreadsheet, the tolerance-based %GRR is anchored to the right number, and you can show where it came from.

Second, it holds the gauge’s calibration status at the moment the study ran. A %GRR against either denominator is worthless if the gauge was out of calibration when the parts were measured. PrüfDesk’s auto-calculated calibration due dates keep the gauge current, and its configurable overdue blocking — hard block or soft warning per tenant — keeps an overdue gauge off the study by policy rather than by luck. The as-found/as-left record proves the gauge was in tolerance across the study window.

Around that, the workflow assembles the evidence: reusable calibration procedure templates so every gauge of a type is verified the same way, a check-out and allocation audit trail that proves which serial was in the study, and audit-ready PDF reports that pull the certificate, traceability, and tolerance into one file. When the customer asks for the tolerance-based %GRR and the proof the gauge was in-cal at study time, you answer with a document, not a scramble.

A short pre-submission check

• Does your MSA summary state clearly whether each %GRR is %Tolerance or %Study Variation?
• For every inspection/release gauge, is the %Tolerance number reported, not just %SV?
• Is the tolerance in the study the current drawing value, traceable to the spec of record?
• Was the gauge in calibration for the entire study window, with the certificate on file?
• Can you produce the calibration status and traceability for that serial in one retrievable package?

If the answer to the first two is "I’d have to check the template," that’s the number your customer will question first.

One study really does give two verdicts. Report the denominator that matches the gauge’s job, name it plainly, and stand it on a gauge you can prove was in calibration when the parts were measured. If you’d like to see how PrüfDesk holds the tolerance and the in-cal evidence that make your %GRR defensible, it’s worth a look before your next PPAP submission — not after the SQE’s email.