The Fallout Shelter FAQ, Section 6: Incidents

https://github.com/therabidsquirel/The-Fallout-Shelter-FAQ/wiki/Section-6:-Incidents

Community FAQ. Internal incidents (fires, radroaches, mole rats, radscorpions) and external attacks (raiders, feral ghouls, deathclaws); a background timer raises incident chance until one is guaranteed, and a failed rush resets it; minimum population per incident type; incidents spread only from empty rooms and never revisit a room; strength rises with average dweller level, then room level, then room width; no incidents while the game is not in the foreground.

Fallout Shelter