If an event occurs and involves a surprise shit and is not offensive, then it is a happenshit.
If you found a bag of flaming dog shit at your front door, you might report the shitcident to your homeowners' association. ... I wouldn't if I were you, though. You probably deserved it.
When a cat can't make the catbox and is imitating Pollock on the walls with shit smears, you point and exclaim, "Is this fucking shitcident because of you, Mr. Pussy McFluffypants?!"