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

Select the method or formula of your choice.

## EMP statistics for the ANOVA method

Test-retest error (Repeatability)
The test-retest error in the EMP statistics table is the square root of the test-retest error variance in the variance components table.

(Repeatability)0.5 = (MSRepeatability)0.5

Degrees of freedom
The degrees of freedom depend on whether the analysis includes the Part*Operator interaction. Without the interaction, the analysis uses the following formula:
DF = (abn – 1) – (a – 1) – (b – 1)
With the interaction, the analysis uses the following formula:
DF = (abn – 1) – (a – 1) – (b – 1) – [(a – 1) × (b – 1)]
The formulas use the following definitions:
TermDescription
anumber of parts
bnumber of operators
nnumber of replicates
Probable error
0.674490 * (Repeatability)0.5

### Intraclass correlation

Use the variance components to calculate the intraclass correlation. The value of the intraclass correlation determines the gage classification.
Intraclass correlation (no bias)
Part / (Part + Test re-test error)
Intraclass correlation (with bias)
Part / (Part + Test re-test error + Operator)
Intraclass correlation (with bias and interaction)
Part / (Part + Test re-test error + Operator + Part*Operator)
Bias impact
Intraclass correlation (no bias) – Intraclass correlation (with bias)
Bias and interaction impact
Intraclass correlation (no bias) – Intraclass correlation (with bias and interaction)

## EMP statistics for the Xbar-R method

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).
Degrees of freedom
The calculation of the degrees of freedom is from Appendix C1. In cases where the degrees of freedom are not on the table in Appendix C, use the following formula:
v' = v + cd * (g' – g)
TermDescription
v the degrees of freedom for g subgroups, which also depends on the subgroup size
cdthe value of cd from the table for g subgroups, which also depends on the subgroup size
g'(the number of operators) * (the number of parts)
gthe largest number of subgroups that is in the table, 20
Probable error
0.674490 * (Repeatability)0.5

### Intraclass correlation

Use the variance components to calculate the intraclass correlation. The value of the intraclass correlation determines the gage classification.
Intraclass correlation (no bias)
Part / (Part + Test re-test error)
Intraclass correlation (with bias)
Part / (Part + Test re-test error + Operator)
Bias impact
Intraclass correlation (no bias) – Intraclass correlation (with bias)
1 Automotive Industry Action Group (AIAG) (2010). Measurement Systems Analysis Reference Manual, 4th edition. Chrysler, Ford, General Motors Supplier Quality Requirements Task Force