Bill,
Over the past couple of weeks I've been measuring a part in one of our shops that we have been doing assembly work on, and I noticed some repeatability problems that I did not see in the lab.
I have a 5' gold arm mounted on a 2.5 foot tall Brunsen stand. I am measuring 3 tooling balls and one surface to measure a line. The three tooling balls create a plane and a circle and the line is aligned to the Y direction. I then go back and check the location of each tooling ball. What I found was, that on some checks, balls were out up to .020". I traced most of my problem to the Brunsen stand where I did not have things as tight as they should have been. But I did notice that if I had the brunsen stand off to the side so that I was making a maximum reach with the arm then I had more problems with repeatability than if I had the stand directly in front of the part and making smaller arm movements.
So to summarize I would do the repeatability check with the arm at maximum extent ion and with your holding device aligned to it's weakest point.
Bob Connors
Lawrence Berkeley National Lab