@statman you raise a really good point here. Probably in most cases we would want the noise (RMSE) in the experiment to reflect typical process variation because we really do want to understand if the treatment effects are large relative to what we would expect typically in production. If we are running say, 3 replicates over the duration of a 15 or 20 run DOE -- one near the beginning, one near the middle and one near the end -- and if on average we are getting "similar" results with little spread, then we have some reasonable indication that the measurement process is stable.
But how much spread is a "little"? A Gauge R&R should help us consider a way to baseline the precision of our measurement method for Y, perhaps even before we do a DOE (for process characterization and discovery). If we can characterize the repeatability and reproducibility (precision) of the measurement system in Gauge R&R, at least we have a baseline for what we determine as 'acceptable precision' in the measurement of Y before running that DOE. Of course we could do this concurrently with a DOE. It all really depends -- in my mind on things like the 'robustness' of the measurement system (which depends on things like: how well we've characterized it before, how complex we believe the system is, how much we understand about the interaction of the measurement system with the part of interest which may or may not be in scope the Gauge R&R study... & that's another one up for debate!)