Just to add to Victor's explanation more generally, every analysis of data is dependent on how the data was acquired. What questions you can answer, what tools should be used for analysis, conclusions from the analysis, confidence in the ability to extrapolate the conclusions, etc. all depend on how the data was acquired.
If there is a hierarchy (nested) relationship between the columns, that hierarchy must be respected in the analysis. The order of the terms in the model is important (Sequential vs. Partial SS). If the columns are crossed, there is no hierarchy and interactions between the columns can be estimated.
For your explanation, I also am a bit confused...Each component you listed needs to be better described. Typically, Operator, lot, instrument and run will be nested in site. Unless you are using the same lots across sites? Are these incoming lots of material/parts or are they being manufactured at each site? Additionally are instruments confounded with operators (each operator haas their on instrument) or crossed (every operator uses every instrument)?
I recommend drawing a tree diagram that describes how the samples were obtained and measured. Use coding of the values for each component, but be careful the actual numbers you use (is every number unique or are there repeated patterns in the component. For example (not for your specific example):
![Screen Shot 2022-07-01 at 10.19.05 AM.jpg Screen Shot 2022-07-01 at 10.19.05 AM.jpg](https://community.jmp.com/t5/image/serverpage/image-id/43733iC477E3CE94A35B6C/image-size/medium?v=v2&px=400)
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![Screen Shot 2022-07-01 at 10.19.34 AM.jpg Screen Shot 2022-07-01 at 10.19.34 AM.jpg](https://community.jmp.com/t5/image/serverpage/image-id/43734iA73A1337FACB40A9/image-size/medium?v=v2&px=400)
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"All models are wrong, some are useful" G.E.P. Box