I do not understand your situation. Here are my thoughts (mostly questions):
1. Are you measuring the "several thousand parts" in the exact same location or is the within part variation confounded with measurement precision repeatability? Are you not interested in other measurement system elements (e.g., discrimination, reproducibility, stability, bias, accuracy)?
2. Why are you measuring the parts 10 times? This is a subgroup size of 10 which seems excessive to get an estimate.
3. While you can easily calculate summary statistics for the subgroups, one of the key aspects of EMP is to look at the data graphically and assess the consistency of the within subgroup variation BEFORE any summary statistics are calculated.
4. I don't understand what you mean by "define the spec of this type of dataset"? The spec should be related to customer requirements (theoretically form, fit and function).
"All models are wrong, some are useful" G.E.P. Box