aterpster
Two different issues. You flip a coin and over many flips it will be heads 50% of the time. Same idea with your 20-sided dice.
If it is like the roll of a dice, we better get rid of RNP AR before someone hits a mountain.
Unfortunately the rnp error probability is very nearly the same as a simple dice roll. The only difference is that a 20-sided dice has a
definite 5% probability of giving any one particular number. Conversely, the rnp has an
indeterminate 5% probability of being wrong at any one time. The rnp probability cannot be definite, because there are too many variables involved, and each variable has its own probability of being in error. And you will probably need a series of incorrect variables to coincide before you find yourself off track. But the total probability of error is still up to a maximum 5% chance of being off track at any one time.
And your highlight of 'population of aircraft' does not help with the probabilities, because each individual aircraft is a part of the population and therefore a part of the probability matrix. Having 5% of aircraft being probably off track, is exactly the same as saying your individual chance of being probably off track is 5%. You cannot say that any one 20-sided dice, out of 1,000 such dice, is excluded from the probability matrix.
Put it this way. If the probability of an excursion away from 0.3 nm rnp were one in 100,000 flights, as you intimated, the manufacturer of GNS systems would say:
... rnp 0.3 is expected to be achieved at least 99.999% of the flight time.
but they do not, they say:
... rnp 0.3 is expected to be achieved at least 95% of the flight time.
There is a good reason for that very large 95% caveat. The total GNS system, including all the many variables and disturbances that go together to determine the probability of your position, is not as reliable as many pilots seem to think. Especially if you are weaving through high terrain.
1,000 ft decision, anyone....?