Gage R&R Calculator — ANOVA and Average-and-Range Methods

Both published methods, because they disagree

The ANOVA method fits a two-way crossed random-effects model with part and operator both random. It is the default, it is the only one of the two that can separate a part×operator interaction from repeatability, and its variance components come straight out of the mean squares.

The average-and-range method turns three ranges into three standard deviations using the K factors: EV = R̄̄·K₁, AV = √((X̄_diff·K₂)² − EV²/(parts × trials)), PV = R_p·K₃. It is older, it is what most shop-floor forms are printed for, and it is not an approximation to the ANOVA answer.

On the same ninety readings they report 27.86 % and 26.68 % study variation — and, more consequentially, four distinct categories and five. The guidance asks for at least five. One method passes this gauge and the other fails it, so both are computed on every run and the one you did not select is printed underneath as a cross-check.

The K factors are computed, not typed in from a table

K₁ is 1/d₂ at the number of trials. K₂ and K₃ are 1/d₂*(m, 1), where d₂*(m, g) = √(d₂² + d₃²/g) — the small-sample form, at g = 1, because each of those two comes from a single range rather than an average of many.

That distinction is the thing a hand-built spreadsheet gets wrong. At two operators d₂*(2,1) is exactly √2, giving K₂ = 0.7071, where plain d₂ would give 0.8862 — a 25 % difference straight into the reproducibility estimate. The values this tool computes reproduce the published table to all four decimals it prints, and the figure names them.

ndc is truncated, not rounded

The number of distinct categories is 1.41 × (part σ̂ ÷ gage R&R σ̂), and the result is truncated to a whole number. On the shipped study that is 4.86, which is four categories — not five. The widely quoted guidance asks for at least five, so the convention decides the verdict.

The 1.41 is itself a rounding of √2. The two land either side of the line often enough that the multiplier is an option here, and whichever one produced the answer is printed on the figure with the untruncated value beside it.

The interaction term, and the two thresholds

The ANOVA method fits part×operator, tests it, and drops it if it is not significant — pooling its sum of squares into repeatability and refitting. The threshold matters: the published manual’s rule is p ≥ 0.25, and the market-leading software defaults to 0.05. Both are offered here, the p-value is printed, and the figure names the model that was actually fitted.

Keeping a term that should have been dropped raises the repeatability estimate; dropping one that should have stayed hides an operator who measures some parts differently from others. The interaction panel is where you can see which it is: parallel lines mean no interaction.

Reading the six panels — two of them backwards

The R chart must be IN control. A cell range beyond its limit means an operator failed to repeat on that part, and nothing else on the figure is worth reading until that is explained. The shipped study has exactly one, and the tool flags it.

The X̄ chart should be OUT of control. Its limits are drawn from repeatability, so points sitting inside them mean the gauge cannot tell the parts apart. A tidy averages chart here is the bad outcome, which is the opposite of every other control chart on this site — and the reason the caption is printed under the panel.

The remaining four: components of variation compares the percentages against each other; measurement by part shows the spread the gauge has to resolve; measurement by operator shows reproducibility as a step; and the interaction panel shows whether the operators disagree consistently or only on some parts.

What this tool will not do

It will not analyse an unbalanced study. If a part × operator cell is missing a trial it refuses and names the cell, because an unbalanced crossed design has no single published method and quietly analysing the parts that happen to be complete is how a gauge gets approved on nine parts that were never meant to stand alone.

It will not decide whether your gauge passes. It prints the criteria, it prints all three percentages and ndc, and it prints one line saying the decision is yours and your customer’s. Acceptance is a contractual matter, not an arithmetic one.

It will not silently return a negative variance. Method-of-moments components go negative whenever a mean square falls below the one beneath it. They are set to zero, which is the convention, and every clamp is marked on the table and explained under the figure — because a reproducibility that reads 0.00 % because the model did not fit looks identical to one that reads 0.00 % because the operators agreed.

Common questions

Which percentage should I quote?

The one your customer’s form asks for, and say which it is. If the characteristic has a tolerance and the print specifies one, %Tolerance is usually what is wanted. If you are comparing the gauge against the process, %StudyVar is the standard-deviation ratio and %Contribution is the variance ratio. All three are on the figure with their denominators, precisely so the answer travels with the question.

Why does my ndc differ from the software we use?

Three things move it: the method (ANOVA and average-and-range give a different PV/GRR ratio — on the study shipped here, four categories against five), the multiplier (1.41 as printed, or √2), and truncation. Truncation is not optional in the published definition: 4.86 is four. Every one of the three is printed on the figure.

My repeatability disagrees with another package. Why?

Almost always the interaction term. A package that drops part×operator at p ≥ 0.05 and one that drops it at p ≥ 0.25 fit different models, and the repeatability estimate is the difference between MS(error) and the pooled mean square. Switch the threshold here to match theirs and the numbers should meet; the figure prints the p-value and the model either way.

How many parts, operators and trials do I need?

Ten parts, three operators and three trials is the usual study, and it is what the guidance assumes. This tool accepts any balanced design from two parts up and warns when yours is smaller, because below that the components come from few degrees of freedom and will move on a repeat study. The parts should span the range the process actually produces — a study on ten identical parts measures nothing about part-to-part variation.

Can I use this for a PPAP submission?

The arithmetic is reproduced against two public worked examples and every constant is computed rather than tabled, and you can check both on the validation page. Whether that satisfies your customer, and whether the acceptance decision is defensible, is between you and them under your own quality system. This is a calculation aid, not a disposition authority, and it says so on every figure it draws.

Is my data uploaded anywhere?

No. The whole calculation runs as JavaScript in this browser tab. Gauge study data is customer part data, which most quality agreements forbid putting into a cloud service — and nothing on this site accepts any of it.