An interesting debate. All based on mathematical concepts and theories.
BUT.
Having spent many years in technical fields (too many?), it is may contention that maths has NOTHING to do with the probability of failure of components. The ONLY law that applies universally is Murphys, which basically states (paraphrased) that:
A component will fail when:
1) It is at its most inconvenient,
2) It will do the most damage,
3) All of the above.
and no mathematical algorythm will ever be able to predict it happening.
Cynical I know, but it works in the majority of cases and if it doesn't at some stage, it's only to cause maximum embarrassment to someone expressing the theory.