Repeatability and reproducibility are the two parts of measurement error that a Gauge R&R study separates from real part-to-part differences. Repeatability is the scatter you get when the same operator measures the same part again with the same gauge, and reproducibility is the extra scatter between operators. An ANOVA-based study, the method the AIAG MSA manual recommends, partitions the variance into equipment, operator and part-to-part components. Until your own study, run on your parts under your conditions, confirms the vendor’s accuracy figures, treat them as unverified.
A bad %GRR can come from a poor gauge, but it can also come from a narrow part sample or from reading the wrong ratio. The sections below cover how to read the decomposition, how to tell those causes apart, and what to write into the contract.
How an ANOVA Gauge R&R splits repeatability, reproducibility and part variation
An ANOVA Gauge R&R fits a crossed random-effects model to a balanced study in which several appraisers each measure every part more than once. The model splits the variance into four sources: parts, operators, the operator-by-part interaction, and the residual repeatability error of the gauge itself. Reproducibility is the operator variance plus the interaction variance, repeatability is the residual mean square, and the two together form the total Gauge R&R variance. Total variation is that Gauge R&R variance plus the part-to-part variance.
ANOVA explicitly models the operator-by-part interaction, which the older Average and Range method does not. ANOVA does not assume the interaction is zero. When the interaction is real, ANOVA counts it in the Gauge R&R, so the percentage comes out higher than an Average and Range calculation on the same data would give. A significant interaction means appraisers measure particular parts differently, and on an interaction plot it shows up as crossing lines. It points to fixturing or part loading, where part orientation changes from one operator to the next.
When to pool the interaction term
When the interaction is not significant, it can be pooled into the error term. The AIAG manual drops the operator-by-part term when its p-value is above 0.25, while Minitab’s default cut-off is 0.05. Many software packages offer the 0.25 option and fold the interaction into equipment variation when they use it. A vendor report should therefore say which threshold it used, and your study should use the same one.
Crossed or nested design
A crossed design only works when every operator can measure every part, because that structure is what lets repeatability, reproducibility and the interaction be told apart. When that structure is not achievable, the crossed analysis does not fail loudly. It returns numbers that look ordinary and are wrong. Destructive tests, where a part cannot be measured twice, and setups where units cannot be shared between appraisers call for a nested design instead.
How big the study needs to be
The AIAG standard design is at least 10 parts, 3 operators and 2 replications, which gives 60 measurements. The recommended design is 10 × 3 × 3, which gives 90. Parts should be measured in random order. Without randomisation, fatigue, drift and learning effects load onto the appraiser term and push reproducibility upward.
The standard design gives imprecise estimates of part-to-part and reproducibility variation. It needs approximately 35 parts for 90% confidence of estimating part-to-part variation within 20% of the true value, and about 135 parts for 10%. Repeatability is better served: the 10 × 3 × 2 design gives 30 degrees of freedom for error, which is close to the roughly 35 needed for a 20% margin. In a Minitab simulation of ten-part studies on a gauge with a true overall %Contribution of 5.88%, about 1 in 4 studies failed the gauge. Two or three operators are not enough for a precise reproducibility estimate. Ask the vendor for confidence intervals on every component, because those intervals show how much uncertainty sits behind the headline figure.
Repeatability versus reproducibility: which one blames the gauge
Repeatability (equipment variation, EV) reflects the gauge’s resolution, mechanical condition and consistency. Reproducibility (appraiser variation, AV) reflects how operators differ in technique, loading and reading. If reproducibility is poor while repeatability is acceptable, the likely cause is the lack of a standard measurement procedure, not the hardware.
The fixes differ to match. High EV calls for gauge maintenance or replacement, better fixturing, environmental control or better resolution. High AV calls for a documented work instruction, operator training or a positioning aid. One caution: repeatability still contains operator behaviour, because a person runs the repeated measurements. Two operators can also have very different individual spreads and the same average, which hides a repeatability problem if you look only at reproducibility. Control charts staged by operator show that pattern.
On an automated vision station, the presentations varied may be operators loading, shifts or days. Define the appraiser factor before the study starts.
How do I interpret Gauge R&R results, and what %GRR is acceptable?
The AIAG MSA 4th Edition sets two criteria, and a study must meet both. %GRR below 10% passes. Between 10% and 30% is conditional and can be accepted with documented customer approval when the characteristic is not safety-critical and the process has capability margin. 30% or higher is not acceptable, and a number of distinct categories (NDC) below 5 fails the study on its own.
Check which column you are reading before comparing it with those bands. They apply to Gauge R&R as a percentage of study variation or of tolerance. They do not apply to %Contribution, which is built from variances and uses bands of 1% and 9%. %Contribution values add up to 100, and %Study Variation values do not.
The two band-bearing ratios answer different questions. Percent study variation compares measurement variation with the spread of the parts you sampled, so it is the right check when the measurement feeds control charts and capability studies. Percent tolerance compares measurement variation with the specification width, so it is the right check for release or acceptance decisions. It is calculated as 6 × the Gauge R&R standard deviation divided by the tolerance. With a 0.10 mm tolerance and a 0.005 mm Gauge R&R standard deviation, the gauge consumes 30% of the tolerance. Percent tolerance does not move with the part sample, which is why it is the number to quote when a gauge sorts parts against a specification. For a station that accepts or rejects product, we would make %tolerance the contractual headline and report %study variation beside it.
NDC, the second criterion, flags problems that a good-looking %GRR hides. NDC = 1.41 × (PV / GRR), where PV is the part-to-part standard deviation, and it counts the statistically distinct groups the system can separate within the part variation. An NDC of 1 means the system cannot tell parts apart, an NDC of 2 means it can roughly sort them into high and low, and 5 or more supports real process-control decisions. %GRR can look good while NDC is low when the parts are very similar. %GRR can also look marginal while NDC is high when the part spread is wide, so the two must be read together. Below 2, the system is effectively an attribute gauge that can sort pass from fail but cannot rank parts.
The case against the AIAG bands
Not everyone accepts the bands. One critique, drawing on Donald Wheeler’s work, argues that the AIAG percentages treat standard-deviation ratios as if they were proportions. Only variances add, so on that argument a measurement system with a %GRR of up to 45% can still be a “First Class” process monitor. Its advice is to drop the AIAG criteria in favour of Wheeler’s classes of monitors. Its premise that only variances add is mathematically sound. The practical step is to name the statistic and its basis (standard deviation or variance) in the contract, so that neither side can switch scales later.
%GRR failed: is it the gauge or the parts in the study?
Before blaming the gauge, check whether the study parts actually span the range the process produces. If the parts come from the middle of the process distribution, the part-to-part variation in the study shrinks. The denominator of %GRR, total variation, shrinks with it, while the measurement-system numerator stays the same, so the study makes the gauge look worse than it is. Parts from a single lot cause exactly this. The ANOVA model assumes the parts are a random sample of the production population, so a narrow panel inflates %Study Variation.
There is a telling special case. An NDC below 5 alongside a %GRR below 10% signals that the study parts were too homogeneous. The fix is to rerun with parts spanning the full production tolerance range, not to adjust the gauge. If the system has been in service for some time, the historical process standard deviation can stand in for the small sample’s estimate of total variation.
A rejected study usually comes down to one of three causes: the study design did not match the process, the wrong acceptance ratio was used, or the system genuinely cannot resolve the tolerance. The third is the least common. Work through them in order. Check the design first, then the appraiser contribution, then repeatability, then the interaction, and only then make a documented risk-based decision on a borderline result.
Diagnostic table: reading a failing study
| What the study shows | Likely cause | Response |
|---|---|---|
| High %GRR, low NDC, parts drawn from one lot or the middle of the range | Narrow part sample | Rerun with parts spanning the full production range |
| NDC below 5 but %GRR below 10% | Parts too homogeneous | Rerun with wider parts; do not adjust the gauge |
| Fails %study variation, passes %tolerance | Wrong ratio for an acceptance decision | Report %tolerance for conformance decisions |
| AV dominates | Operator technique or procedure | Write a work instruction, train, add a positioning aid, rerun |
| EV dominates | Gauge instability, fixture wear, resolution | Hardware fix or a different gauge |
| Significant operator-by-part interaction | Part loading or orientation varies | Redesign the measurement procedure |
| Fails %tolerance, %study variation and NDC on a well-sampled, correct design | Genuine gauge failure | Average repeats (repeatability falls by √n) or invest |
After any corrective action, repeat the study to confirm it meets the criteria before the system goes back into production use.
What Gauge R&R study to run on a vendor’s inspection station before sign-off
The study to run before signing for a vendor’s inspection station depends on what the station outputs. If it reports a dimension, run an ANOVA variable Gauge R&R on parts that span your real process range. If it makes pass/fail calls, run an attribute agreement analysis against known-good and known-bad reference parts instead of a variable Gauge R&R.
LynxBenchAI benchmarks hardware performance, not a vendor’s classifier: look up the station’s device on LynxBenchAI to see its measured results.
Attribute agreement for a pass/fail station
Attribute agreement analysis asks whether each appraiser agrees with itself across trials, with the known standard, and with the other appraisers. AIAG measurement systems analysis guidance, as summarised by SPC for Excel, treats an attribute system as acceptable when effectiveness is above 90%, the miss rate below 2% and false alarms below 5%. Effectiveness of 80% to 90%, a 2% to 5% miss rate or 5% to 10% false alarms count as marginal. A kappa above 0.75 reads as good to excellent agreement and below 0.40 as poor.
To build the sample, start with a master set of roughly half good and half defective parts, including borderline parts on both sides of the limit, each with a reference decision set against the customer’s standard. Every part then goes through the station several times, in random order, at production speed, across at least two presentations such as different loaders, shifts or days. If you use the AIAG analytic method for an attribute gauge instead, its requirements are strict: a known reference value for each part, at least 8 parts at roughly equal intervals spanning the process range, and 20 trials per part.
VDI/VDE/VDMA 2632 Part 3, issued in October 2017, introduced indicators of classification capability for vision systems whose results are attributes. Part 3.1, published in August 2020, describes methods for checking classification performance and helps users and suppliers choose a procedure for acceptance tests. A headline like “99% accuracy” means little until you know which metric was measured, on which defect classes and under what production conditions. Ask for defect prevalence, recall, precision, escape rate, false reject rate and the number of samples tested. Our separate piece on validating a model’s accuracy and confidence claims before you rely on them goes deeper on the model-side metrics.
Run the study on site. A shadow run, where the AI runs beside the existing inspection without triggering rejects, lets you compare its calls with actual decisions before it controls anything. Your own inspectors need a baseline too: if they agree with one another only 85% of the time, labels built on their judgement cap the consistency any model can demonstrate. The inspection criteria need clarifying before the model can be judged fairly against that baseline.
Acceptance criteria and remedies when your numbers disagree with the vendor’s
In our judgement, the protocol belongs in the contract before any data is collected. That means the part set, how reference decisions are set, the number of trials and presentations, the statistic that counts (%tolerance or %study variation, standard-deviation or variance basis), and the interaction-pooling threshold. Results can be disputed on methodological grounds unless both sides agreed the method in advance. Acceptance thresholds should be stated in measured terms: a %GRR or %tolerance ceiling plus an NDC floor for measuring stations, and miss-rate, false-alarm and effectiveness limits for pass/fail stations. Add a tolerance band within which your figures count as agreeing with the vendor’s, sized with the study’s confidence intervals in mind.
If your results fall outside the band, the contract should lay out the steps in order:
- A joint re-test under the agreed protocol, with the master parts held under change control.
- A vendor remediation period with a fixed deadline.
- Payment holdback or a price adjustment while the shortfall stands.
- Exit or termination rights if remediation fails.
Signing as-is and hoping the gap closes is the weakest of the available positions.
A single study does not cover later process or product changes. The Embernet guidance is to repeat the study after every significant model change and on a calendar schedule, with master parts controlled like calibration standards. Write that cadence in as an ongoing service-level term, not a one-time acceptance event. More generally, MSA is a prerequisite for quality decisions, not a one-time setup activity.
When a third-party metrology audit is worth commissioning
An internal study, well designed and documented, is the default, and often it is enough. We would reserve it for three situations: your results and the vendor’s are both inconclusive (wide intervals, borderline bands); the disagreement is large enough that you need independent evidence that will hold up in a dispute; or the characteristic is safety-critical and the multi-year commitment is large. Where the station measures dimensions, we would look to an accredited metrology lab. Where it classifies defects, look for an auditor who can work to the VDI/VDE/VDMA 2632 Part 3.1 acceptance methods.
Who can help us verify a vendor’s AI inspection station before we sign?
TechnoLynx verifies AI inspection stations through production AI reliability work, which is distinct from headline accuracy. Validation packages for the classifier are part of Production AI Reliability.
For a station that is a conventional measuring gauge with no learned model in the loop, an accredited metrology lab or an experienced quality engineer running the AIAG study is the more direct route.
FAQ
Are repeatability and precision the same?
Not quite. Precision describes how tightly repeated measurements cluster, whether or not they sit near the true value. Repeatability is the precision under identical conditions (same operator, part and gauge), and reproducibility is the part of precision lost when the operator changes.
How do you calculate repeatability in an ANOVA study?
In the ANOVA method, the repeatability variance is the residual (error) mean square from the crossed model. Its square root gives the equipment-variation standard deviation, which software then scales to %study variation or %tolerance.
