Gage R&R explained (with a worked example)

Short answer: a gage R&R study tells you how much of the variation you see is coming from the measurement system and not from the parts. If the gage is noisy, you can't tell good parts from bad ones, and your control charts and capability numbers can't be trusted.

• Repeatability (equipment variation, EV): one operator measures the same part several times with the same gage. The scatter is repeatability.
• Reproducibility (appraiser variation, AV): different operators measure the same parts. The difference between operators' averages is reproducibility.
• GRR combines the two: σ²_GRR = σ²_{repeatability} + σ²_{reproducibility}.

How a typical study runs

Pick about 10 parts that cover the real process range. Have 2 or 3 operators measure each part 2 or 3 times, in random order, without seeing earlier readings. Then analyze the data with the ANOVA method (preferred, because it also gives the operator × part interaction) or the average-and-range method.

Worked example

The ANOVA gives these standard deviations: repeatability 0.030 mm, reproducibility 0.020 mm, part-to-part 0.150 mm. The tolerance is 1.0 mm wide.

What it means: by the common rule of thumb (under 10% good, 10–30% may be acceptable depending on the application, over 30% unacceptable) this gage is marginal. With ndc = 5 it can separate parts into enough groups for process control (5 or more is the usual target). Repeatability is the bigger piece, so look at the gage itself first: fixturing, resolution, cleanliness, wear. If reproducibility were bigger, you'd look at training and method.

Common exam traps

• Adding standard deviations. Variances add; standard deviations don't. Square, add, then take the root.
• Mixing up %study variation and %tolerance. One compares the gage to the process spread, the other compares it to the spec width. They answer different questions.
• Picking parts from a narrow range. If all study parts are nearly identical, part variation looks tiny and %GRR looks terrible, even with a good gage.
• Confusing accuracy with precision. GRR is precision. Bias, linearity and stability are separate studies.
• Ignoring resolution. A rough rule: the gage should resolve at least one tenth of the tolerance or process spread.

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