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
d_{2}
d_{2} = d_{2}* 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
d_{2}
d_{2} = d_{2}* from Appendix C^{1}. 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,
d_{2}
d_{2} = d_{2}* from Appendix C^{1}. 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