The headline result is 6.93% Total Gage R&R—comfortably inside the familiar 10% guideline. That makes the measurement system generally acceptable, but it is not the end of the review.
The same analysis also finds a measurable operator effect and an operator-by-part interaction close to the usual 0.05 significance level. Those details do not overturn the result, because their practical contribution is small beside real part-to-part variation. They do tell the engineer what to verify before formally releasing the method.
This worked example follows the full decision: understand the study design, inspect the repeated readings, review the Gage Evaluation table, read the six diagnostic charts, and decide what action the evidence supports.
The measurement system is generally acceptable.
Total Gage R&R is 6.93% of study variation, Gage R&R consumes 7.99% of the 1.000 mm tolerance, and ndc is 20. The asterisk is important: standardize or verify the small operator shift and borderline interaction before using the result for a high-risk release decision.
Do not translate 6.93% into “93.07% accurate.” Gage R&R estimates the spread created by the measurement process. Accuracy, bias, calibration, linearity, stability, and measurement validity require their own evidence.
Evidence supporting acceptance
- Total Gage R&R is below 10% of study variation.
- %Tolerance is also below 10%.
- ndc is 20, well above the common minimum of 5.
- Part-to-part variation clearly exceeds measurement variation.
- Repeated ranges remain inside the R-chart limits.
Evidence requiring follow-up
- Operator means rise from 50.0068 to 50.0268 mm.
- The ANOVA operator term is statistically significant.
- Operator × part interaction is borderline at p = 0.0495.
- Part sampling and randomized measurement order still need confirmation.
- The intended decision risk determines whether follow-up is advisory or mandatory.
1. What study was performed?
The example evaluates a digital micrometer used to measure a diameter with specification limits from 49.500 to 50.500 mm. Three operators each measure the same ten parts three times. Because every operator measures every part, this is a crossed Gage R&R study.
The balanced design produces 3 operators × 10 parts × 3 trials = 90 readings. Repeated readings inside each operator-part cell estimate repeatability. Differences between operator averages estimate the operator component of reproducibility. Because the study has repeated measurements for every operator-part combination, crossed ANOVA can also estimate operator × part interaction.
Why part selection matters
A study can appear artificially strong when the selected parts span an unrealistically wide range. %Study Variation becomes smaller when the part-to-part denominator grows, and ndc rises for the same reason. The selected parts therefore need to represent the variation the gage will encounter in routine work—not simply the widest parts available.
For this prepared sample, the ten part means range from 49.7521 to 50.3038 mm. That provides a strong part signal while remaining inside the stated specifications. In a production study, the engineer should document where the parts came from, whether they represent expected long-term variation, and whether the measurement sequence was randomized.
View all 90 measurements
| Part | Operator A | Operator B | Operator C | Part mean | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| T1 | T2 | T3 | T1 | T2 | T3 | T1 | T2 | T3 | ||
| 1 | 49.761 | 49.761 | 49.769 | 49.789 | 49.784 | 49.785 | 49.800 | 49.807 | 49.793 | 49.7832 |
| 2 | 50.100 | 50.093 | 50.108 | 50.115 | 50.122 | 50.123 | 50.142 | 50.138 | 50.131 | 50.1191 |
| 3 | 49.912 | 49.907 | 49.901 | 49.907 | 49.900 | 49.909 | 49.922 | 49.924 | 49.913 | 49.9106 |
| 4 | 50.244 | 50.227 | 50.237 | 50.222 | 50.249 | 50.232 | 50.250 | 50.238 | 50.249 | 50.2387 |
| 5 | 49.753 | 49.734 | 49.739 | 49.765 | 49.751 | 49.744 | 49.763 | 49.760 | 49.760 | 49.7521 |
| 6 | 50.049 | 50.033 | 50.049 | 50.044 | 50.059 | 50.048 | 50.056 | 50.066 | 50.065 | 50.0521 |
| 7 | 49.850 | 49.851 | 49.854 | 49.869 | 49.869 | 49.868 | 49.866 | 49.858 | 49.883 | 49.8631 |
| 8 | 50.179 | 50.160 | 50.149 | 50.182 | 50.191 | 50.176 | 50.184 | 50.187 | 50.195 | 50.1781 |
| 9 | 49.967 | 49.951 | 49.967 | 49.981 | 49.964 | 49.970 | 49.976 | 49.992 | 49.975 | 49.9714 |
| 10 | 50.305 | 50.292 | 50.302 | 50.318 | 50.308 | 50.297 | 50.304 | 50.311 | 50.297 | 50.3038 |
2. How does ANOVA separate the variation?
A percentage alone cannot tell us where measurement variation comes from. Crossed ANOVA decomposes the observed variation into part, operator, operator × part, and repeatability terms. MSA Studio retains the interaction term in this example rather than pooling it into repeatability.
Variation among the three readings made by the same operator on the same part becomes the within-cell or equipment component.
Systematic differences among the three operator averages contribute to reproducibility.
This term captures whether operators disagree differently depending on which part is measured.
Repeatability and reproducibility variances are added, then converted to a standard deviation and 6σ study variation.
Total Gage R&R is divided by total study variation; the same 6σ gage spread is also compared with the 1.000 mm tolerance.
Method note: this product report uses study variation = 6 × standard deviation. The separate Average & Range calculation guide explains its own constants and calculation trail. Do not expect results from different methods or spread conventions to match digit for digit.
3. The actual MSA Studio report
The report below is generated from the same sample and chart logic used in Mechatrovich MSA Studio v1.3.1. It is not a simplified article illustration. Hover chart marks to inspect the underlying values.
Gage R&R (ANOVA) Report for Diameter
Crossed study with operator × part interaction · MSA Studio v1.3.1
| Source | StdDev (SD) | Study Var (6 × SD) | %Study Var (%SV) | %Tolerance (SV/Toler) |
|---|---|---|---|---|
| Total Gage R&R | 0.013313 | 0.079877 | 6.93 | 7.99 |
| Repeatability | 0.007976 | 0.047854 | 4.15 | 4.79 |
| Reproducibility | 0.010659 | 0.063955 | 5.55 | 6.40 |
| Operators | 0.009851 | 0.059108 | 5.13 | 5.91 |
| Operator × Part | 0.004070 | 0.024423 | 2.12 | 2.44 |
| Part-to-Part | 0.191713 | 1.150280 | 99.76 | 115.03 |
| Total Variation | 0.192175 | 1.153050 | 100.00 | 115.30 |
Components of Variation
Measurements by Parts
R Chart by Operators
Measurements by Operators
Xbar Chart by Operators
Parts × Operators Interaction
Report-level reading: the gage consumes a small share of the observed variation and tolerance, while the selected parts create a strong signal. The diagnostic charts support acceptance, but they also show why operator consistency should still be checked.
4. What each diagnostic chart tells us
The six graphs answer different questions. Treating the component percentage as the complete analysis would hide the operator pattern and the study-execution checks that matter most after the initial pass.
Total Gage R&R contributes only 0.48% of variance and 6.93% of study variation. Part-to-part variation represents 99.76% of study variation. Both %Study Variation and %Tolerance support the headline acceptance decision.
The ten groups are separated clearly, and the repeated points inside each part remain tight. The mean line changes substantially from part to part, while repeated readings occupy a comparatively small vertical band.
The average range is 0.01387 mm and the upper range limit is approximately 0.03569 mm. The largest observed range is 0.030 mm, so no operator-part cell exceeds the control limit. There is no isolated repeatability spike demanding immediate investigation.
The distributions overlap strongly because every operator measures the same broad part set. Their means are not identical: A = 50.0068, B = 50.0180, and C = 50.0268 mm. The 0.0200 mm A-to-C shift is small relative to tolerance, but systematic enough to investigate.
Many subgroup means fall outside the calculated Xbar limits. In a Gage R&R chart, this is usually desirable: it shows the measurement system can distinguish parts. This is not a process-control chart, so “points outside the limits” should not be interpreted as process instability.
The lines broadly follow the same part pattern, but they are not perfectly parallel. ANOVA estimates a small interaction component of 2.12% study variation, with p = 0.0495. Because that value sits near the conventional 0.05 boundary, the practical pattern and study execution matter more than declaring a binary statistical verdict.
5. Why “acceptable” still includes an operator check
The ANOVA operator term has F = 26.69 and p < 0.001, while operator × part interaction has F = 1.78 and p = 0.0495. Statistical significance answers whether the observed pattern is unlikely under a no-effect model. It does not answer whether the effect is large enough to make the measurement system unusable.
| Source | DF | Mean square | F | p-value | Practical reading |
|---|---|---|---|---|---|
| Part | 9 | 0.330899 | 2920.11 | <0.001 | Very strong part signal |
| Operator | 2 | 0.003025 | 26.69 | <0.001 | Small systematic offset exists |
| Operator × Part | 18 | 0.000113 | 1.78 | 0.0495 | Small, borderline interaction |
| Repeatability | 60 | 0.000064 | — | — | Low within-cell variation |
The operator shift uses only 2% of the 1.000 mm specification width. It is not large enough to overturn the overall Gage R&R result, but it is systematic enough to check zeroing, contact force, measurement location, fixture use, and work-instruction interpretation.
6. How should the familiar 10% and 30% bands be used?
The bands are screening guidance, not universal release criteria. Measurement risk depends on what the result will support. A study used for internal process improvement may tolerate more uncertainty than a safety-critical acceptance decision or a characteristic very close to a specification limit.
This example falls below 10% on both comparisons: 6.93% of study variation and 7.99% of tolerance. ndc = 20 also indicates that the gage can distinguish substantially more than the commonly used minimum of five categories across the selected part range.
A strong ndc does not validate the sampling. Because ndc depends on the ratio of part variation to gage variation, an unrepresentatively wide part set can inflate it. Confirm the part-selection rationale before treating 20 as a production capability statement.
7. What would I decide as the engineer?
I would classify this measurement system as generally acceptable for the demonstrated range and tolerance, with a targeted operator-method follow-up. The evidence does not justify rejecting the gage: measurement variation is small, repeatability is stable, %Tolerance is low, and the part signal is strong. It does justify closing the operator questions before a high-risk or customer-facing approval.
Confirm randomization, blinding, normal production fixturing, environmental conditions, and that operators did not see earlier readings.
Observe zeroing, contact force, measurement location, part cleaning, alignment, and how each operator interprets the work instruction.
Use a reference or master part to see whether the A-to-C shift is repeatable and linked to technique, setup, or instrument handling.
If the review identifies a correctable method difference, update the standard and repeat the study after the change. Do not rerun studies simply until a preferred p-value appears.
For routine process analysis, the current evidence may be sufficient. For critical conformance decisions, document the follow-up and apply the customer or company approval method.
Continue with the study
Use the free browser calculator for a quick crossed-study check, or use MSA Studio when you need the full ANOVA workflow, the six diagnostic charts shown above, Average & Range analysis, and a printable report.
Measurement-system analysis is the first step.
The Quality Engineering Suite also includes SPC and process-capability tools for the next stages of the analysis.
Limitations of this worked example
This is a prepared educational dataset. It demonstrates interpretation, but it cannot confirm that a real study used representative parts, a valid measurement definition, adequate calibration, randomized order, normal operating conditions, or the required customer-specific procedure. Gage R&R also does not replace separate assessments of bias, linearity, stability, or measurement uncertainty where those are required.
For foundational definitions, study planning, and common failure modes, continue to Gage R&R Basics. For the explicit constants and formula trail used in a smaller Average & Range example, use the Gage R&R Average & Range Calculation.
References and method sources
- AIAG, Measurement Systems Analysis (MSA), 4th Edition — industry reference for measurement-system assessment and improvement.
- NIST/SEMATECH e-Handbook, Gauge R&R Studies — design and analysis considerations for production measurement systems.
- NIST, Analysis of Repeatability — interpretation and graphical review of repeatability variation.