Am I missing something. Every derating analysis I have ever been in contact with was done analytically.
My last job was derating analysis and it was done analytically; so this is a correct statement.
Some was worst case where we built the circuits in MicroCap and ran a Monte Carlo analysis. Most of our analysis seemed theoretical at best and wasn't the ideal job for me due to being repetitive and not hands on.
In most cases we took an agreed upon derating factor for the design based on the customer needs and just created endless monotonous spreadsheets. As an example, all capacitors shall be derated 50% (the agreed percentage based on customer needs), so we'd create a spreadsheet with all the parts, enter the derating factors, the voltage/temp/etc... and see if anything was out of this specification. The final result would be a report along with a dumbed down fancy spreadsheet.
The Monte Carlo analysis would run many loops changing values based on the component tolerances.
Then we also conducted reports based on some list of numbers that were created (nobody in the department knew their origin but some were based off of NASA specs). It would add all the component numbers from the list based on failure rate, blah blah, and tell us the device as a whole would last at minimum the X years the customer wanted the unit to run for (similar to how commercial electronic specifications state they are good for X thousand hours (i.e. MTBF).
My personal input was most of this was all fluff and felt the numbers just appeased the customer. My feeling of projected life expectancy is a calculated risk that a percentage of failures may occur in less than say 100k hours that would outweigh the profits made on units that met the minimum and/or the customer would "upgrade" thus reliving the company of early failures.
Monte Carlo analysis was somewhat fun, but the circuits may have components that were created such as a delayed switch to simulate charging rates. So the "ideal" component was nothing more than a calculated charge/discharge rate.