Gage R&R explained: repeatability, reproducibility and a study example
One operator repeats a reading closely. Another gets a different result on the same part. Inspect the individual measurements before changing the production process.
Gage R&R means gage repeatability and reproducibility. It examines variation from repeated measurement under the same conditions and from changes such as the operator. It is part of measurement system analysis, often shortened to MSA. Gage is also written gauge. The worked example shows how to read these patterns before planning a full study.
A shaft measures 9.980 mm at one inspection station and 10.020 mm when another operator checks it. The part hasn't been machined again between readings.
Adjusting production now could be a response to the measuring method rather than the shaft.
ASQ's explanation separates repeated readings by one operator from differences between operators measuring the same part. The measuring process includes how the instrument is positioned and used, not just the instrument itself.
Gage repeatability vs reproducibility
Repeatability asks how closely one operator can repeat the measurement of the same characteristic on the same part with the same instrument and method.
Reproducibility examines changes across conditions included in the study. In a common crossed Gage R&R study, every operator measures every part, so operator-related differences can be examined without giving each person a different set of parts.
| Pattern in the readings | What it suggests checking |
|---|---|
| One operator's repeats on the same part are widely spread | Positioning, contact force, fixturing, instrument condition and other within-method variation |
| Each operator repeats closely, but their averages differ | Differences in technique, interpretation or setup between operators |
| Operators agree and repeat closely, but all miss a reference value | Bias relative to that reference, a separate concern from R&R |
Use these patterns to choose what to investigate. To judge accuracy, you also need a suitable reference.
Gage R&R study example: inspect 27 readings
Our teaching example has three stable parts, one instrument and three operators. Each operator measures every part three times, giving 27 readings. The values are constructed so the different patterns are easy to see.
Start with “Operators apart”. The repeats cluster tightly, but operator A reads lower and C reads higher on every part. Switch to “Repeats spread” to see a different problem while the operator averages agree.
Same parts, different measurement patterns
Look inside the average
Three trials per operator on each part. The thin vertical line is the assigned reference for that part. Values are millimetres.
Repeat measurement spread0.005 mmPooled within-group sample standard deviation
Highest minus lowest operator mean0.040 mmObserved mean range, not a reproducibility SD
Scroll sideways to inspect the complete measurement scale. Every reading is also in the table below.
Operators apart
Each operator repeats closely, yet A reads lower and C higher on the same parts. Check the shared method before choosing which reading to act on.
Overall mean minus assigned reference: 0.000 mm. Opposite operator offsets can cancel in this overall mean.
| Part | Assigned reference | Operator A | Operator B | Operator C |
|---|---|---|---|---|
| 1 | 9.900 | 9.875 / 9.880 / 9.885 | 9.895 / 9.900 / 9.905 | 9.915 / 9.920 / 9.925 |
| 2 | 10.000 | 9.975 / 9.980 / 9.985 | 9.995 / 10.000 / 10.005 | 10.015 / 10.020 / 10.025 |
| 3 | 10.100 | 10.075 / 10.080 / 10.085 | 10.095 / 10.100 / 10.105 | 10.115 / 10.120 / 10.125 |
| Overall mean | 10.000 | 9.980 | 10.000 | 10.020 |
How the examples and summaries are calculated
Assigned part references are 9.900, 10.000 and 10.100 mm. “Operators apart” adds offsets −0.020, 0 and +0.020 mm for A, B and C, with repeat deviations −0.005, 0 and +0.005 mm. “Repeats spread” removes operator offsets and uses repeat deviations −0.020, 0 and +0.020 mm. “Common shift” adds 0.030 mm to all references with repeat deviations −0.005, 0 and +0.005 mm.
Within each of nine part/operator groups, squared deviations from its mean are summed. Pooling divides the total by 9 × (3 − 1) = 18 degrees of freedom; its square root is the displayed sample SD. The operator gap subtracts the lowest overall operator mean from the highest, using the same three parts and nine readings per operator. This range is not a variance estimate. A complete R&R analysis and a pass/fail decision need further work.
Each pattern deliberately repeats the same structure across parts. Real studies need representative sampling, randomised collection, uncertainty assessment and checks for interaction and time effects.
In the first case, A's readings on part 2 are 9.975, 9.980 and 9.985 mm. Their mean is 9.980. The sample standard deviation is 0.005 mm, which describes the spread of those repeats around their mean.
Within one part-and-operator group
Sample variance = (0.005² + 0² + 0.005²) ÷ (3 − 1) = 0.000025 mm²
Sample standard deviation = √0.000025 = 0.005 mm
Every group has that same constructed spread. Pooling their within-group variances therefore also gives 0.005 mm. NIST's repeatability guidance explains pooling when the groups can appropriately share a precision estimate.
Across the same three parts, the operators' overall means are 9.980, 10.000 and 10.020 mm. Their range is 0.040 mm. This is not a standard deviation, so adding it to 0.005 mm would not calculate total R&R.
Repeatability, reproducibility and measurement bias
Choose “Common shift”. The operators now agree closely with one another, yet all their means sit 0.030 mm above the example's assigned reference values. The repeatability stays at 0.005 mm.
A real bias check needs a suitable reference and its uncertainty. The assigned values here are fictional teaching references. Tight clusters alone cannot show whether a real measurement is close to the value it should represent.
NIST's gauge-study framework treats repeatability, reproducibility, bias, resolution and stability as distinct concerns. Passing one check doesn't settle the others.
Plan the study around the measurement decision
Three convenient parts are too narrow a basis for judging a production measuring system. Choose parts that represent the variation relevant to the job and operators who represent ordinary use. Keep the characteristic, fixture, method and instrument scope clear.
Minitab's crossed-study guidance recommends at least ten parts, three operators and two repeats as a common starting layout, with more parts useful when process variation is poorly known. The design still needs to fit the actual system and any required method.
Randomise the part order within each repeat and retain the individual readings. Don't let operators copy earlier results. If testing destroys or changes the part, a crossed design using the identical part may not be possible; select an appropriate alternative.
A full analysis also needs to examine whether operators differ more on some parts than others. Our constructed offsets are the same for every part, so they don't demonstrate that interaction. Changes over days or shifts need suitable time coverage too.
Use the finding before adjusting the machine
If the evidence points to a positioning difference, agree and test the locating method with the operators. If repeated readings scatter, investigate the repeat measurement conditions. Buying a finer display won't automatically fix either problem.
Compare the result with the decision the measurement must support. Sorting near a specification boundary and monitoring process changes may need different assessments. A percentage without its denominator and agreed acceptance criteria is an incomplete result.
Acceptance sampling makes a separate decision about a lot using the inspection results; it assumes that classification is credible.
The Cp and Cpk note is the next step when the measurement is credible enough to assess process capability. Keep the measurement method and units with those quality records, especially after a fixture or gauge change.
For the shaft that started this example, remeasure the same identified parts under a planned comparison before changing the machining setting. Otherwise, a measurement disagreement can become an unnecessary production adjustment.
Sources and example notes
- ASQ: Gage Repeatability and Reproducibility. Definitions and crossed-study structure.
- NIST: Gauge R&R studies and analysis of repeatability. Separate measurement concerns and pooling within-group variances.
- Minitab: Crossed Gage R&R data considerations. Representative parts and operators, repeat measurements and randomisation.
Readings and reference values are fictional. The tool summarises repeat variation, operator means and differences from the assigned references. A full R&R analysis needs a suitable study design and variance estimates.