# Methods and formulas for variance components in Evaluate Measurement Process (EMP Crossed)

Select the method or formula of your choice.

## Variance components for the ANOVA method

The variance components in the table depend on whether the p-value for the Part*Operator interaction is less than the significance level for the analysis. By default, the significance level is 0.05. To change the significance level, choose File > Options > Control Charts and Quality Tools > Gage R&R Study, then change the value in Alpha to remove interaction term.

Test-Retest Error (Repeatability)

Repeatability = MSRepeatability

Operator (Reproducibility)
The calculation of the component includes the Part*Operator interaction when the interaction is statistically significant. With the interaction, the analysis uses the following formula:
Without the interaction, the analysis uses the following formula:
TermDescription
anumber of parts
nnumber of replicates
Part*Operator (Reproducibility)
TermDescription
nnumber of replicates
Part (Product variation)
The calculation of the component includes the Part*Operator interaction when the interaction is statistically significant. With the interaction, the analysis uses the following formula:
Without the interaction, the analysis uses the following formula:
TermDescription
bnumber of operators
nnumber of replicates
Total
When the analysis includes the interaction, the variance component for reproducibility includes the variance component for the operators and the variance component for the interaction. When the analysis does not include the interaction, the variance component for reproducibility is the variance component for the operators.
Total Variation = VarCompRepeatability + VarCompReproducibility + VarCompProduct variation

## Variance components for the Xbar and R method

The variance is the square of the standard deviation.

Test-Retest Error (Repeatability)
Equipment variation, the standard deviation is calculated as:

TermDescription
anumber of parts
knumber of operators
Rijrange of measurements by operator j for part i
d2d2 = d2* from Appendix C 1. When looking for this value, use g = (# of parts) * (# of operators) and m = (# of replicates).
Operator (Reproducibility)

Operator variation, the standard deviation is calculated as:

TermDescription
the average measurement for operator i
anumber of parts
knumber of operators
nthe number of repeated measurements on a part by one operator
d2d2 = d2* from Appendix C1. When looking for this value, use g = 1 and m = (# of operators).
Part (Product Variation)

The standard deviation is calculated as:

TermDescription
Rprange of part average values,
d2d2 = d2* from Appendix C1. When looking for this value, use g = 1 and m = (# of parts).
nthe number of repeated measurements on a part by one operator
knumber of operators
anumber of parts
Total Gage R&R

The standard deviation is calculated as:

Total Variation

The standard deviation is calculated as:

1 Automotive Industry Action Group (AIAG) (2010). Measurement Systems Analysis Reference Manual, 4th edition. Chrysler, Ford, General Motors Supplier Quality Requirements Task Force