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
| ソース | SS | df | MS | Variance estimate |
|---|---|---|---|---|
| パート | — | — | — | — |
| Operator | — | — | — | — |
| Part×operator | — | — | — | — |
| 再現性 | — | — | — | — |
Balanced crossed random-effects model
σ²e=MSe
σ²PO=max[(MSPO−MSe)/r,0]
σ²お=max[(MSお−MSPO)/(pr),0]
σ²P=max[(MSP−MSPO)/(or),0]
σ²GRR=σ²e+σ²お+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.
解釈
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.
