How this calculation works
A measurement system can vary when the same operator repeats a reading, when operators change, and when operators respond differently to particular parts. A crossed gage study separates these sources under a random-effects model. This page uses balanced replicated part-by-operator data and retains the interaction component. It reports gage standard deviation separately from part-to-part variation rather than mixing all observed spread into one number.
Balanced crossed ANOVA: repeat variance=MSE; interaction=(MSinteraction−MSE)/r; operator=(MSoperator−MSinteraction)/(parts×r); truncate negative componentsA worked example
The constructed example has two parts centered at ten and twenty, two operators, and repeat errors −1 and +1 in each cell. Residual mean square is two; operator and interaction mean squares are zero. Gage standard deviation is √2, while part variance is fifty under the stated unpooled truncation convention. Gage fraction of total modeled variance is two divided by fifty-two, about 0.0384615.
Good to know
Only a balanced crossed random-effects layout is supported. Missing cells, nested operators, destructive testing and repeated drift require different models. No percent-of-tolerance result or universal pass/fail cutoff is supplied. The arithmetic does not approve a measurement system or establish that its study design was representative.
Reference: SAS — gage variance component method (opens in a new tab) ↗
What this calculation answers
A measurement system can vary when the same operator repeats a reading, when operators change, and when operators respond differently to particular parts. A crossed gage study separates these sources under a random-effects model.
This page uses balanced replicated part-by-operator data and retains the interaction component. It reports gage standard deviation separately from part-to-part variation rather than mixing all observed spread into one number.
The Correlated measurement uncertainty budget calculator combines uncertainty contributions. A crossed gage study estimates particular repeatability, operator and interaction variance components from a balanced experiment.
Use the right input conventions
Each row identifies a part, an operator, a repeat label and a measurement. Every part-operator cell must have the same two-to-ten repeat count, with unique labels within its cell. At least two parts and two operators are required.
All measurements share units and procedures. The study should represent the parts and operators of interest; a narrow or deliberately extreme part selection can change interpretation of variance percentages.
Interpret the result
Repeatability is the residual variance. Reproducibility includes operator and part-by-operator interaction. Negative method-of-moments variance estimates are truncated individually to zero, without pooling interaction or refitting the ANOVA.
This convention can differ from software that drops a nonsignificant interaction and recomputes components. The page states its method so numerical disagreement is investigated as a modeling choice rather than hidden by matching labels.
Work through the example
The constructed example has two parts centered at ten and twenty, two operators, and repeat errors −1 and +1 in each cell. Residual mean square is two; operator and interaction mean squares are zero.
Gage standard deviation is √2, while part variance is fifty under the stated unpooled truncation convention. Gage fraction of total modeled variance is two divided by fifty-two, about 0.0384615.
Where the model stops
Only a balanced crossed random-effects layout is supported. Missing cells, nested operators, destructive testing and repeated drift require different models.
No percent-of-tolerance result or universal pass/fail cutoff is supplied. The arithmetic does not approve a measurement system or establish that its study design was representative.
A few questions, answered
Does this pool a small interaction into repeat error?
No. Interaction remains in the model and negative variance estimates are truncated separately at zero.
What changes in the comparison?
Change one repeated reading to inspect its effect on repeatability and interaction estimates.