Balanced crossed replicated study
Crossed Random-Effects Gage R&R ANOVA
Estimate variance components for part,operator,operator×part interaction and repeatability with a fully disclosed method-of-moments two-way ANOVA. No automatic acceptance decision is made.
Variance-component estimates
| Source | SS | df | MS | Variance estimate |
|---|---|---|---|---|
| Part | — | — | — | — |
| Operator | — | — | — | — |
| Part×operator | — | — | — | — |
| Repeatability | — | — | — | — |
Balanced crossed random-effects model
σ²e=MSe
σ²PO=max[(MSPO−MSe)/r,0]
σ²O=max[(MSO−MSPO)/(pr),0]
σ²P=max[(MSP−MSPO)/(or),0]
σ²GRR=σ²e+σ²O+σ²PO
p,o and r are the numbers of parts,operators and trials. Components are in squared measurement units; displayed σ values are their square roots. Negative method-of-moments component estimates are reported in the note and truncated to zero for the combined nonnegative variance display.
Open statistical sources
NIST/SEMATECH e-Handbook §3.2.3.2 gives the balanced crossed two-way model and sums of squares for part,operator,interaction and residual. NIST/SEMATECH e-Handbook §7.4.4 explains random effects,expected mean squares and method-of-moments variance components.
Standards and acceptance boundary
ISO5725-1:2023,edition2 provides general principles and definitions for trueness and precision and explicitly says calculation methods are in other parts; this calculator does not claim to implement ISO5725. AIAG MSA 4th edition is a separately licensed manual. Because its full licensed method was not available for this audit,the former 10/30% labels,ndc coefficient/threshold and minimum-study claims are not implemented or presented as verified.
Interpretation
GRR/total study variation and variance contribution are descriptive for the sampled part population; changing the selected parts can change them. They are not percentages of tolerance and no pass/warn/fail class is assigned. Confirm study design,assumptions,customer requirements and the governing licensed procedure before making a measurement-system decision.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
