common mode failures
"Grunf, I think you are referring to the design criteria of a failure per 10^9 operational hours. You also mention probability. The probability of all three ADIRU's failing at once is more like 10^9*10^9*10^9!"
in the analysis of failure probability for redundant systems the concept of common mode failure is used (in the nuclear industry at least) to invalidate the chaining of probabilities such as suggested here. This recognises that anaysis is based on a 'model' of reality, not reality itself. I gather reading this forum that such failures have been observed rarely but often enough that 1 in 10^9 itself seems 'optimistic'.
Incidentally, one common mode failure path could be disruption through excessive vibration, I seem to remember reading that another version of similar equipment (different make) had problems in this respect before (hitting a mounting shelf ?) for which the existence of ISIS was a mitigating factor.
With all the systems which rely on inertial sensors, I would think that it is not possible to reset these in conditions where the aircraft is experiencing angular or linear accelerations above quite small limits owing to the need to find the direction of true 'g'.