Does this calculator certify AIAG MSA acceptance?

No. It reports transparent crossed random-effects ANOVA estimates and makes no automatic acceptance decision. AIAG MSA criteria require the licensed manual and the applicable customer or quality-system requirements.

What design is required?

A balanced crossed study: every selected operator measures every selected part the same number of repeated trials. The model assumes random representative part and operator levels,independent approximately normal residuals and constant repeatability variance.

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.

Two-way crossed ANOVAInteraction retainedNo AIAG conformance claim

Variance-component estimates

Repeatability σ_e

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Operator σ_O

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Operator×part σ_PO

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Reproducibility √(σ²_O+σ²_PO)

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Combined Gage R&R σ_GRR

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Part-to-part σ_P

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Total study σ_total

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GRR / total study variation

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GRR variance contribution

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Source	SS	df	MS	Variance estimate
Part	—	—	—	—
Operator	—	—	—	—
Part×operator	—	—	—	—
Repeatability	—	—	—	—

Balanced crossed random-effects model

y_ijk=μ+P_i+O_j+(PO)_ij+e_ijk
σ²_e=MS_e
σ²_PO=max[(MS_PO−MS_e)/r,0]
σ²_O=max[(MS_O−MS_PO)/(pr),0]
σ²_P=max[(MS_P−MS_PO)/(or),0]
σ²_GRR=σ²_e+σ²_O+σ²_PO

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.