Unkle put some good accurate information there.
One thing that is missing is that proof of a cord, cable, chain, hose, etc, is all based on static numbers. 100 pounds will break that rope, 400 on the chain, etc. A firearm isn't any bit that precise. You have a high spike of pressure at first, the pressure tapers off as the barrel does, approximately. Just look at a standard rifle to see the approximate curve representing needed strength.
The problem with thinking in a straight line for proof pressures and max pressures is that there are too many variables in shooting. Another problem is that there are so many variables in firearms themselves. A proof load must be calibrated to give a clear indication that the firearm is capable of not only holding the peak pressure in, but also maintain pressure integrity throughout the whole trip down the barrel. The proof test isn't just about whether the barrel splits, it is also testing bolt lugs, receiver integrity, etc. Lots of small things can fail during an over charge shot.
as nick said, though, what must be worried about more than anything is the slow degradation of structural integrity. You can run over maximum loads in a gun for years without blowing it up, and actually be slowly tearing it apart. The bolt lugs and the receiver slots can be peening, fatigue cracks can be forming in various places, etc. We can understand and accept that a throat will eventually wear out, that a .458 will eventually loosen in the stock, and many other things, but it's a little harder to understand that your steel parts may eventually loosen and stretch as a constant diet of overpressure rounds are fed through it.
One of my friends when I was young had his grandfather's old military 38 revolver. The thing had splits in the barrel by the cylinder. He had +p ammo in it at the time, but it also turned out that the cylinder was straight bored. I don't know what caused the cracking. Obviously this 60-80 year old pistol was made of weaker steel. The cylinder may have had .357 rounds run through it, there may have been too many +p, the thing may have had a barrel obstruction, etc. The point is that this thing appeared to have very serious material failures, but it has not had a catastrophic failure. Most people look for only a Kaboom, and never consider that there could be other, serious damage occurring in longer term.
Why would a .300 magnum go into suck spectacular catastrophic failure? Did the guy forget to clean out his powder measure and dump a half load of bullseye into his first charge?
