Borderlands – “Roid damage”

As you said, these are all the pieces already. If what I'd figure is your question it's easy to answer: "How much damage would I do if I fire for $Length time?"

$Length * $RoF = X rounds
X rounds * $damage = gunDamage
X rounds * $DOT% = avgDotAmount

DoTs are smart in this game, they all have their separate timers and can stack independently from one another. This makes the damage as intuitive as possible:

dotDamage = avgDotAmount * ticks(element)
totalDamage = (gunDamage + dotDamage) * multiplier(element)

As this was far too easy to answer, I can only assume your question would be like
"When can I stop firing, knowing that my DoTs will kill the enemy?" To which the answer would be "Never, unless the target isn't currently affected, then keep firing."

To us human player at least; for all the data is there in the fountain of numbers that spew from the target you are perforating with bullets. Would we be perfect computers, we could see when a new dot starts ticking(it wouldn't have a previous tick before it) and thus know exactly how many ticks are left. Being human, all we can say is "it's on fire" or "it's not on fire." This makes knowing for SURE your target is going to die impossible, the best one could do is make a normal distribution graph(wiki) with the probabilities if your target will die.

If that's really what you'd want, I could run it through some model, but it's still gonna be a pretty useless graph. Input the specific gun and skills you're using, and you could get a graph with probabilities mapped vs dotDamage. Even if you could watch that while shooting things, you can only guess how much health your target has left.

If instead, and my final guess, the question would be "How much do I overkill?" that amounts to the same, as that is also "Amount of dotDamage still to be done."

Yes and no. As I eluded to in the comments, this takes effect only with "electrocute" Damage Over Time effects. Whether or not they're a result of your skills or guns doesn't matter, it just has to be electric DOT caused by you (deathtrap counts as you).

How it really works is every time an enemy takes electrocute Damage Over Time, there's a chance they'll catch fire, too. It never seems to start upon the initial hit with a Shock attack, and it can happen if you stop shooting but let the enemy fry for a second. Most of Gaige's electrical skills will induce Damage Over Time, so many of them have a chance to burn as well.