Barrel bulging/bursting can be pretty much understood from hoop stress analysis. Barrel ID, wall thikness and pressure are the factors for this quite simple calculation. To fully understand what goes on with barrel stress, you have to also know the barrel wall thickness profile and the pressure vs distance curve. These two are not exactly simple. Then, you need to understand the barrel material's strength properties. And, lastly, you need to know the barrel material's fatigue properties.
Your generic shotgun barrel has sufficient safety factor to withstand proof pressure at a very high level of confidence (very, very few barrels bulge/burst in proof). Also, steel is a good material for fatigue resistance. Although I haven't done actual fatigue analysis on a shotgun barrel, I'd bet sporting money on near infinite fatigue life.
Obstruction ruled out, we are pretty much left with thin spots or inclusions/discontinuities that act as stress risers within the material. CH pointed out that the technology to find very small inclusions is not available/practicle for shotgun barrels. If the stress riser acts to increase the actual stress within the steel near the riser sufficiently, we can get into a fatigue situation. How close the stress comes to ultimate tensile strength for the barrel material determines the fatigue life. One failure senario would be a lot of cycles that had heavily fatigued a thin spot or an inclusion followed by a load that produced unusually high pressure.
