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

Select the method or formula of your choice.

In This Topic

Variance components for the ANOVA method
Variance components for the Xbar and R method

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 = MS_{Repeatability}

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:

Term	Description
a	number of parts
n	number of replicates

Part*Operator (Reproducibility)

Term	Description
n	number 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:

Term	Description
b	number of operators
n	number 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 = VarComp_{Repeatability} + VarComp_{Reproducibility} + VarComp_{Product
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:

Term	Description
a	number of parts
k	number of operators
R_ij	range of measurements by operator j for part i
d₂	d₂ = 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:

Term	Description
	the average measurement for operator i
a	number of parts
k	number of operators
n	the number of repeated measurements on a part by one operator
d₂	d₂ = 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:

Term	Description
R_p	range of part average values,
d₂	d₂ = d₂* from Appendix C¹. When looking for this value, use g = 1 and m = (# of parts).
n	the number of repeated measurements on a part by one operator
k	number of operators
a	number 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