Short answer: no.
Long answer: The ANOVA you are fitting is probably a random effects ANOVA, with the Part effect being random. Maybe you have other random terms as well, such as time effects, operator effects, materials, gauges, setups, etc. Maybe one of those effects should be the nominal value of the part. Then you can model the variance as a function of the nominal value (and other terms) and you don't have to assume equal variances. If the nominal values are really far apart, consider doing a separate analysis for each range. For example, if you have parts at 10, 1000, and 10000, you might perform three separate analyses.
In JMP, if all your effects are random, you can use the EMP or Variability platforms to get those variance components. If some effects are fixed and others are random, use Analyze > Fit Model to specify the mixed model and get the variance components.
I hope this helps!
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