> a more academic treatment
Academics are OK, even if I work for some.
But capacitors are a combination of theory and manufacturing reality. Your 99.9% pure aluminum... what's that other 0.1% crap? Is it the same crap as the foil you bought last year? Is 500ppm copper benign? Is 2ppm thorium toxic to the oxide? Did Joe sneeze in the vat of electrolyte?
You find out by tests. You could run a 7-year test before selling the caps from that batch, but that does not work well because of inventory capital and inventory shelf-rot. The only practical test is to put them in an oven for 7-week and 7-month testing, and pray that Arrhenius was right. Field experience says it is usually true-enough for small changes like 20degC. With the long life of modern caps, it is impractical to wait hundreds of thousands of hours to verify the low-temp life: by the time you have confirmation, the factory has changed the product so much you can't get the exact-same caps and you can't be sure some low-temp worm has not snuck into the new product.
And obviously the 10degC rule does not extend to infinity. An older Compaq PC in an unheated garage in the northern US will fail to start because the caps ESR is too high for the switcher, but 20 minutes of sitting stalled and an off/on cycle will bring it up. Perhaps the caps "meet specs" but Compaq did not design for this environment. Or they tested new caps in a cold-room, but did not realize that cold-ESR would rise over time (or didn't care after the warranty period). It is not a hard failure, but if you NEED the PC *now*, it is a failure. OTOH, a simple passive PSU with these high-ESR caps would "work" with extra ripple which might decline by the time you are ready to record... not a practical failure.
> I would like to be able to quantify the risk involved.
If you have a big budget, the cap-makers would like you to call their engineers. They don't want you to DIY a guesstimate, buy their caps, be wrong, and get unhappy. The major makers have guys who think caps all day long.
If you have a little budget, call. You might reach a guy who would be thrilled to talk about caps (cap-engineer must be a lonely life). But respect that he has to justify his time to a company which is barely profitable in these cost-cutting times.
Over at Hoffman's forum there is a late-30s Rickenbacker guitar amp with original caps. It may have hundreds of hours at 70C, and obviously 70 years= 600,000 hours at ~~25C no-volt. Note however that the caps could be way down on original value and still "work", because it has choke and hum-buck in addition to just capacitors. OTOH, a 1937 PA amp I had, the caps were dead-open; however it showed signs of long hot use.
