Peter,
I struggled with the same problem.
When you look from the viewpoint of metrology the theory will be this (according to me):
Y = y ± U
Y = true measurement
y = obeserved measurement
U = expanded uncertainty
U = k u(y)
k = coverage factor (k = 2 for a normal distribution and a probabality of 95%)
u(y) = standard deviation of the total uncertainty of the measurment system
Repeatability and reproducibility are only a part of u(y).
If you have the AIAG MSA Manual 3rd Edition, please have a look at page 61.
More information about uncertainty you can find in EA-4/02 which can be downloaded from the internet, But be aware this paper is very thoeretical.
When you have done a GR&R you can do the following. First you have to make the assumption/statement that the reperatability and reproducibility are the biggest contributors to the total uncertainty. In that case you can use the standard deviation of the repeatability and reproducibility together as u(y). In the MSA Manual 3rd Edition you can use the GRR as mentioned on page 114. This is not true for the 2nd Edition (there the total spread is calculated in stead of the standard deviation).
JeroenM.
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