## Gage R&R Formulas

Repeatability – Equipment Variation (EV%) Repeatability is the variation that occurs when repeated measurements are made by the same operator. This assumes that the operator uses a consistent technique, and that the part is consistent. If these assumptions are true, then the Repeatability Variation is inherent in the measuring instrument itself. $EV\% = \frac{Repeatability\ Std. Dev.}{Total\ Variation\ Std. Dev.} = \frac{EV\sigma}{TV\sigma}$
Reproducibility – Appraiser Variation (AV%) Reproducibility is the variation that occurs due to differences between operators. $AV\% = \frac{Reproducibility\ Std. Dev.}{Total\ Variation\ Std. Dev.} = \frac{AV\sigma}{TV\sigma}$
Interaction – Appraiser by Part Interaction (INT%) The interaction variation is the variation that occurs where the combined effect of the operator and the part is not a simple additive relationship. For example, if one operator tends to have a larger measurement error when measuring small parts than when measuring large parts, whereas everyone else has a similar error, regardless of part size, then we would see an interaction between Operator and Part – This shows up as diverging lines when the measurements are plotted on the same chart.
This term is neglected, and set to zero, unless it is calculated to be statistically significant.
$INT\% = \frac{Interaction\ Std. Dev.}{Total\ Variation\ Std. Dev.} = \frac{INT\sigma}{TV\sigma}$
Gage R&R – (GRR%) Gage R&R is an assessment of the overall variation within the measuring system. So, the gage r&r formula incorporates the variation due to Repeatability, Reproducibility, and Interaction (if it is found to be statistically significant)
$GRR\% = \frac{\sqrt{{EV{\sigma}^2 + {AV\sigma}^2 + {INT\sigma}^2}}}{TV\sigma}$
Part-To-Part Variation (PV%) The variation that occurs due to the variety of parts used in the study. $PV\% = \frac{Part\ To\ Part\ Std. Dev.}{Total\ Variation\ Std. Dev.} = \frac{PV\sigma}{TV\sigma}$
Total Variation – (TV) The total variation from all sources that is observed in the gage r&r study $TV\sigma = \sqrt{{EV{\sigma}^2 + {AV\sigma}^2 + {INT\sigma}^2 + {PV\sigma}^2}}$
Number of Distinct Categories (ndc) If we calculated a confidence interval on the measurement error (GRR), this would give us a measurement error “width”. The ndc is the number of times that a 97% Confidence Interval on the GRR (the width of the measurement error) will fit into the width of the variation due to the parts (or process). It is rounded down to the nearest integer. $ndc = 1.41 \ \frac{PV{\sigma}}{GRR{\sigma}}$
Std. Dev. ${\sigma}$ Estimate of Standard Deviation Standard Deviation