Extremely Remote
Qualitative: Not anticipated to occur to each item during its total life. May occur a few times in the life of an entire system or fleet.
Quantitative: Probability of occurrence per operational hour is less than 1 x 10 -7 but greater than 1 x 10 -9
Extremely Improbable
Qualitative: So unlikely that it is not anticipated to occur during the entire operational life of an entire system or fleet.
Quantitative: Probability of occurrence per operational hour is less than 1 x 10 -9
So should a gearbox be allowed to fail at all? Surely the probability of failure for such a critical component should be Extremely Improbable not just Extremely Remote especially if you are going to sidestep the requirement to prove through testing that it will run for 30 mins (which it failed).
Perhaps the criteria should be based on the likely worst-case human cost - ie 18 pax and crew for a transport aircraft and see how many times that sort of loss can be accepted statisically.