HQRM Testing
Perhaps I'm confused, but it sounds as though you are combining two different issues into a single question. You will indeed want to determine failure probabilities for your total system, probably using some kind of FMEA (failure modes and effects analysis) in order to determine likelihood of failures. MIL-STD-882 gives some pointers. But you need to be careful when you define your 10^-9 figure, since you may mean failure probability per/hour, per flight, for the service life of the fleet of a single customer, or the entire expected production run for the life of the fleet. You've got to decide what you mean and convince the certifying agencies that it makes sense. Regarding actually performing the handling qualities ratings, you'll need to define some representative tasks that require tight control by the pilots, and then evaluate the aircraft during those tasks using multiple pilots with varying flying styles. Lots to do!