A Swedish customer rejected a batch of 340 bearing housings. Their receiving report said five bores were undersize by 0.012 mm. We pulled the same five parts, measured them on our CMM, and every one was in tolerance. Neither side was lying, and neither side was careless. We asked them to run a gage R&R study on their bore gauge, and the answer came back at 38% of the tolerance band. Their measurement system was eating more than a third of the tolerance before the part had any opinion about it.
*(Composite example; details changed.)*
This happens more often than anyone admits, and it is almost never about competence. A gage repeatability and reproducibility study (gage R&R, sometimes written gauge R&R, and abbreviated GR&R) is the standard way to find out how much of what you are reading is the part and how much is the measurement. It takes an afternoon, it costs almost nothing, and it should be run before anyone argues about a dimension.
What the study separates
A gage R&R study splits measurement variation into two pieces:
- Repeatability, or equipment variation (EV). One appraiser, one gauge, one part, measured again. Everything inside that loop lands here, including the instrument, its resolution, the fixturing and the short-term environment.
- Reproducibility, or appraiser variation (AV). A second appraiser, same gauge and same part. Usually technique, and sometimes an appraiser-by-part interaction where two operators disagree about one particular feature rather than about all of them.
Combined, they are GRR. Set against the variation of the parts themselves (PV), you get total variation (TV), and from those you get the two percentages that decide whether the measurement is usable.
| Quantity | Meaning | How it combines |
|---|---|---|
| EV | Equipment variation, repeatability | Spread of repeated trials |
| AV | Appraiser variation, reproducibility | Spread of operator averages |
| GRR | Total gauge variation | sqrt(EV² + AV²) |
| PV | Part variation | Spread of part averages |
| TV | Total study variation | sqrt(GRR² + PV²) |
The two denominators, and why they disagree
Here is the part that causes more arguments than the measurement itself. You can express GRR two ways, and they give different verdicts on the same study.
As a percentage of total variation: %GRR = GRR / TV. This asks whether the gauge can tell two parts apart. It is the number the AIAG MSA manual grades.
As a percentage of tolerance, written %P/T: 100 x GRR / (USL - LSL). This asks whether the gauge is good enough to make an accept or reject decision on this specific tolerance. It is the number a purchasing engineer actually needs.
A worked example, with numbers typical of a bore measurement on aluminum. Every variation term below is quoted as 6 sigma study variation, the convention most MSA software reports: if your package outputs one-standard-deviation components instead, multiply by six before comparing anything with a tolerance band.
| Input | Value |
|---|---|
| Tolerance band on the bore | 0.060 mm |
| EV (repeatability) | 0.006 mm |
| AV (appraiser) | 0.004 mm |
| GRR = sqrt(0.006² + 0.004²) | 0.0072 mm |
| PV (part variation) | 0.030 mm |
| TV = sqrt(0.0072² + 0.030²) | 0.0309 mm |
| %GRR of TV | 23.3% |
| %P/T against tolerance | 12.0% |
| ndc = 1.41 x (PV / GRR), truncated | 5 |
Neither number lands in the acceptable band. At 23.3% of total variation the gauge is marginal: it can tell parts apart, but it is adding real noise. At 12.0% of tolerance it clears the 10% line without much daylight, and that is enough for everyday accept or reject decisions on this bore while still being too weak to support a capability study read off the same instrument, because a gauge that cannot separate parts inflates the observed variation and depresses the reported Cpk. That is the usual trap: a gauge that looks fine against a wide tolerance band quietly ruins the statistics built on top of it.
The conventional grading bands are these:
| %GRR | Verdict |
|---|---|
| Under 10% | Acceptable |
| 10% to 30% | Marginal, may be acceptable depending on the application, the cost of the gauge and the cost of a wrong call |
| Over 30% | Not acceptable, fix the measurement system |
There is a third criterion worth watching: ndc, the number of distinct categories the gauge can resolve, computed as 1.41 x (PV / GRR) and reported truncated to a whole number. Below 5 the gauge sorts parts into fewer than five buckets, and no capability index computed with it means much. Our example calculates to 5.9 and therefore reports as 5, just clearing the usual minimum, which is why the marginal verdict above is survivable.
What actually drives GRR on a shop floor
In our experience the gauge itself is rarely the problem. The top of the list, in the order we find them:
- Part fixturing. The single biggest contributor. A part held by hand, or resting on a surface with a burr under it, moves between trials. On a CMM this shows up as repeatability, and it is not the machine's fault.
- Datum inconsistency. Two operators who establish the datum reference frame differently will disagree by the flatness of the primary datum. On a 200 mm face with 0.04 mm of flatness, that is 0.04 mm of argument with nothing wrong. This is the same trap described in the GD&T true position guide, and it is the reason we write the datum convention on the report, next to the surface roughness callout that governs how the stylus sees the face.
- Temperature. Steel moves 11.5 x 10⁻⁶ per °C, aluminum roughly 23 x 10⁻⁶. A 100 mm aluminum part measured 5 °C above the 20 °C reference is 100 x 23 x 10⁻⁶ x 5 = 0.0115 mm longer than the drawing assumes, against 0.0058 mm for the same part in steel. On a 0.03 mm band the aluminum figure is nearly 40% of the tolerance, and all of it came from the room.
- Surface condition. Burrs, coolant film and a rough finish move the contact point. This is why deburring before inspection is not optional, and the deburring guide covers the edge conditions that move a contact point.
- Operator technique on hand tools. A micrometer on a 12 mm shaft is sensitive to feel, and feel varies. We do not allow calipers on any characteristic with a band under 0.05 mm, and we say so in the inspection plan.
When we run one, and what we hand over
We run a gage R&R on every characteristic the customer classes as special, before the first production run, and again if the gauge, the appraiser group or the measurement method changes. Three appraisers, ten parts representing expected production variation, three trials each: ninety readings, and the analysis runs in the quality system rather than by hand.
What we send back is not just the percentage. It is the method, written plainly enough that the customer can reproduce it: the gauge, the stylus or anvil, how the part is located, the inspection temperature, the material expansion correction and how the datum frame is established. Without that, a GRR number is unfalsifiable, and a disagreement simply moves to the next batch.
If your incoming inspection and our outgoing report disagree, the sequence we suggest is: agree on the datum convention first, check the temperature and the surface condition second, and only then look at the parts. In most of the disagreements we investigate, the parts are acceptable and the measurement method turns out to be the source.
For the equipment side, the CNC inspection methods guide compares what each method can honestly hold. The control plan and capability study guide explains why a gauge that fails a GR&R also invalidates the Cpk computed with it, and how both documents sit inside the first article inspection package.
Frequently asked questions
What is a good gage R&R result?
Under 10% of total variation is acceptable, 10% to 30% is marginal and may be acceptable depending on the application, and above 30% the measurement system needs fixing. Also check that the number of distinct categories is at least 5, because a gauge that can only sort parts into three buckets will not support a capability study whatever the percentage says.
What is the difference between repeatability and reproducibility?
Repeatability is the variation from the gauge and the setup when one operator measures the same part repeatedly. Reproducibility is the variation between operators using the same gauge on the same part. The first is an equipment problem, the second is a technique or training problem, and the study tells you which one you have.
How many parts and operators do you need?
The standard layout is three operators, ten parts and three trials each, for ninety measurements. The ten parts have to represent the variation you actually expect from production, not ten points spread neatly across the specification limits. Artificial extremes inflate PV and make every percentage look better than the gauge deserves.
Can a gage R&R be done with a caliper?
Yes, and that is often how the problem gets found. Hand tools usually have larger repeatability than people expect, particularly on small diameters where feel dominates. If a caliper consumes more than 30% of the band, separate EV from AV before doing anything. Replace the tool when resolution or repeatability dominates, and standardise the method or retrain when appraiser variation is the larger term.
Conclusion
A gage R&R study is the cheapest quality document in the whole package and the one most often skipped. It is ninety readings and an afternoon, and it converts "your numbers are wrong" into "here is where the 0.007 mm is coming from". We run it on every special characteristic, we publish the method with the result, and we would rather run it before the first shipment than after the first rejection.
On features quoted to ±0.01 mm across our 200+ CNC machines, we do not sign off a gauge until GR&R supports the decision it is being used for. That rule has survived 23+ years and three management systems, IATF 16949, ISO 9001 and ISO 13485, largely because arguing about measurement after a rejection costs far more than running the study first. Send us the drawing, the characteristics you care about and the method you use today. We will run the study, set it next to yours, and tell you plainly which number belongs to the part and which belongs to the gauge. DFM is free and a quote comes back within 24 hours. Talk to our team.