The earlier comment about a DGR&R being a nested study is generally the case. Most approaches to GR&R and DGR&R are based on a Random Effects model.
There may be a slightly different way to approach your own situation. Usually 'Part', along with 'Operator' and 'Trial' (which is a unit that is tested for a DGR&R study) are treated as Random Effects. Here, you use Cavity as Part. Cavity probably isn't a valid Random Effect, so I worked up a model that treats it as a Fixed Effect.
The key to understanding these models and making sure the stats are correct is the EMS table. The EMS table tells you how to structure and compare the variance components, and it can be used as a check against the output of your statistical software to be sure the model was treated correctly.
I am attaching an example (attached pdf file). (This example assumes that I read and understood your earlier notes correctly.) My example is based on materials from Montgomery, Perez-Wilson, AIAG, and (for the deeper stats behind the Variance Components model) Searle.
Here is a link to other examples and more information on GR&R, DGR&R, and the underlying Fixed, Random, and Mixed Effects models.
goo.gl/3C2Ov3
(also see the pdf files with specific examples at the bottom of this web page)
Other links that might be of interest:
goo.gl/J7vhsn
goo.gl/TfqEnF
For links, I had to remove the h-t-t-p portion.
Getting the model correct, including the EMS, is critical. If you aren't familiar with these things, you may want to find a local statistician.
Best regards,
Cliff