Performing gage R&R study in R w/more than 2 factors

My guess is that you do not understand the meaning of a "random  
factor". I certainly did not when I first encountered it. All my  
training had been with ordinary regression and analysis of variance.  
These are methods for what in mixed models are fixed effects. My  
opinion is that these terms are completely confusing to the new  
student of this sort of analysis.

You're absolutely right---the distinction of fixed vs. random factors is
confusing. However, I was under the impression that all factors in a
gage R&R study were random, since we're trying to determine the sources
of variability on the system.

My guess is the you may just want the output of:

lm( vals ~ f1 * f2 * f3, data = yourdat)

I'm trying to get the variance component estimates, and from there, I
can calculate the percent tolerance and other interesting statistics. It
doesn't look like lm gives me that information, though. FWIW, your
formula is the same as what I'm feeding into aov, and the ANOVA table
output *does* match up with what Minitab is producing.

Matt