The OP isn't suggesting a random failure when you've been driving without incident.
Think of each major component of the car as having a percentage health/hit points like in many fighting games. You do something that does 35% damage to the transmission and 25% to the engine. Now the probability of failure for the transmission is 35% (65% chance of not failing) and the engine 25% of failing.
The randomness would come into play when one time you can do 40 laps with some amount of damage and next time you can only do 10 assuming you don't do any further damage. These are arbitrary numbers of course but hopefully you get the idea.
It'd be great if you can get performance degrades of the parts as well total failures. For example 0.001% of the 25% engine damage will result in a total failure; otherwise the engine will run at reduce power.