Originally Posted by MountainBear
I find PBLs instance on the math curious because it's Bayes Theorem that says that when presented with statistically rare events we are better off just ignoring those events than trying to solve for them.
Actually, MB, when testing supposedly-ultra-reliable systems, Bayesian methods say that when presented with statistically rare events, such as a failure behavior of the system under test, we are better off throwing the system away and starting again.
Originally Posted by MountainBear
What it tells me is that underneath all the hardheaded talk about math and volumes of proofs lies a warm and beating heart that is ultimate decision maker.
Fine words. But the certification regulations require a case be presented, and if you are a manufacturer of FBW aircraft you have to persuade the regulators that your critical systems have a failure rate of less than 1 in 10^(-9) op-hours. So someone on the manufacturer's side has to do a bit of math to say "here's the argument" and someone on the regulator's side has to follow that math to be able to say "this is a good/insufficient argument". It's easier with hardware, because the properties of hardware are continuous (something breaks; you make it stronger). But it is devilish hard with software. And, humans in it or not, everything in the control loop(s) of a FBW aircraft goes through large amounts of digitally-programmed behavior. You can't expect humans to debug real-time programs magically as they go wrong, if they go wrong. So they had better be right. And that is where the math comes in.
PBL