I will run the risk of getting back to the original question of proofs, which this thread was supposed to be about, remember?
I did some research into failure rates of shotgun barrels both here in the US and at the two British proofing houses as well as the International Proof Commission. Surprisingly enough I could find very little actual data, mostly just discussions and anecdotes. If anyone can provide these data I would be quite interested.
As there relatively few proof houses outside of Europe other than Russian and Japan, I'd think that we would see more failures from countries that produce shotguns that are not subject to proof like Brazil and the US. I can't find many, other than barrels that have been damaged or plugged. I did find these two in the US: WINCHESTER Model 1001, RECALL: Barrels may burst on firing. and SMITH & WESSON Model 916-T SHOTGUNS
RECALL: Smith & Wesson has recalled all barrels for this 12-ga. interchangeable barrel takedown model shotgun because of defect and potential hazard. Barrels may rupture when fired.
Now I've casually looked at some of those weird shotguns that only have one barrel like the Ithaca Model 37 and Winchester Model 12 and they appear to have very thin barrels, although I've never measured one. These types of lightweight repeaters have been made by the millions, all without the "benefit" of proof and seemingly nobody seems to concern themselves with barrel failure and from what I've seen they don't need to based on the billions of rounds that have been shot through them, again apparently with a very, very low failure rate. This is just anecdotal evidence and I'd like to see some data that provides failure rates, especially from the proof houses.
I'm not suggesting that thin barrels are safe! I'm not saying that modified barrels are necessarily safe! I am seeking more hard data.