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Gage R&R calculator

Average and range method. One box per operator: one line per part, with that operator's trials on the line. Every operator must measure the same parts in the same order.

How it is calculated

R̿ = average of every operator's average range per part EV = R̿ × K1 repeatability (equipment variation) AV = √((X̄diff × K2)² − EV²/(n·r)) reproducibility (appraiser variation) GRR = √(EV² + AV²) PV = Rp × K3 part variation (Rp = range of the part averages) TV = √(GRR² + PV²) %GRR = 100 × GRR / TV ndc = 1.41 × PV / GRR (rounded down) %Tolerance = 100 × 6 × GRR / (USL − LSL) Example above: %GRR = 16.8%, ndc = 8, %tolerance = 14.3%

K1 = 1/d₂ for the number of trials; K2 and K3 = 1/d₂* for the number of operators and parts. Published K tables round slightly differently, so results can differ in the third digit. The percentages are shares of the standard deviation, so they do not add to 100%.

Reading the result

%GRRGuidelineTypical action
Under 10%AcceptableUse the gage.
10% to 30%May be acceptableDepends on the use and the cost of a better gage. Fix the larger of EV and AV.
Over 30%Not acceptableImprove the gage or the method before using the data.

Read more: Gage R&R explained · Bias, linearity and stability · Attribute agreement and kappa · MSA for Green Belts

FAQ

What is an acceptable %GRR?

The common guideline: under 10% of study variation is acceptable, 10% to 30% may be acceptable depending on the use and the cost of the gage, and over 30% is not acceptable. The number of distinct categories (ndc) should be 5 or more.

Should I compare to study variation or to tolerance?

Use %study variation when the gage is for process control or improvement, because it tells you whether the gage can see part-to-part differences. Use %tolerance when the gage only sorts good parts from bad. Report the one that fits the job, and say which one it is.

What does a high repeatability (EV) mean?

The same person measuring the same part gets different readings. Look at the gage itself: wear, fixturing, resolution, or the part moving during measurement.

What does a high reproducibility (AV) mean?

Different people get different averages. Look at the method: training, reading technique, clamping force, or a missing work instruction.

Average and range method or ANOVA?

Both estimate the same components. ANOVA also separates the operator-by-part interaction and uses the data more efficiently, so it is preferred when software is available. The average and range method is simpler and is what most exam questions use.

MSA is tested on the CQE and both Six Sigma exams

This shows up on the exams as a calculation question. Practice it with new numbers every time, and every wrong answer explained.

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Free Green Belt diagnostic (20 questions)
Free Black Belt diagnostic (25 questions)

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