In my games, I've used the same system since the late 90s - ever since the first time I heard of the passive perception concept (under a different name, then). There are three rolls for every trap or hazzard: Notice, Understand and Disable. It isn't Rules as Written, but it is just a slight variation on the current rules.
Notice: Passive Perception only gives you the full reveal if you beat the DC by 5. If not, all you get from passive is a hint that something is off. Then a perception roll is required to get the real details of what you're observing. However, all you get are the surface facts - not an understanding of what might be going on outside of what you can directly observe/hear/etc... Sometimes an active roll that fails by too much might set it off.
Understand: Once you have perceived there is something dangerous, you have to do a separate roll to understand how the trap works. This can be arcana, investigation, sleight of hand, thieves tools or some other skill depending upon the trap. Failing by too much sets it off.
Disarm: Then you need to disable it on a third roll. This is often sleight of hand or thieves tools, but could also be arcana, etc... and failing by too much sets it off.
The three DCs will differ from situation to situation. Some might be hard to find (DC 20 perception), easy to understand (DC 12 investigation (set off if you don't get at least a 7)) and difficult to disarm (DC 18 sleight of hand/thieves tools, under 13 sets it off). Others could be easy to find (Perception 5), Impossible to understand (arcana 22, under 15 sets it off), and easy to deactivate (12 arcana to disable, under 10 sets it off).
If the PCs come up with a good reason why a particular skill could be used to understand and/or disable a trap, I just come up with an extra DC on the spot.
This has served me well.