are programmers "failures"?

[Leviset]

Having not written a commercial program since 1991, I did for a few short years head up a System Testing Unit for a large Worldwide Bank. The software was a vanilla suite called Base24 which ran on the new non-stop architecture of Tandem minis.
It had been modified to match the UK Banking Systems and the introduction of Reciprocity between all the UK Banks & Building Societies. I can assure everyone that this was tested to death as software that affects Monetary transactions has always been more important than a few planes falling out of the Sky!
However I seem to remember from my ITIL/ISEB days then there was an algorithm back then (and is still?) that stated that it was not ‘Cost Justified’ to test software to more than 83% of the total 100% possible. I’m pretty sure large Software Houses like Microsoft & IBM played to this rule with customers not knowing that it was ‘cheaper’ to let end users find the remaining ‘bugs’ (if any) and then fix them later with a so called ‘update’ release under the guises of an ‘enhancement release’.
I also remember in the 90s discussions about the Air Traffic Control Systems at Heathrow & Gatwick which used software & hardware in excess of 20 years old and that nobody wanted to take on replacing those systems (I seem to remember that the software ran on either Sperry/Univac or Unisys Mainframes?).
I know we have some pilots on this Forum but do we have anyone who has worked on replacing vintage ATC software & hardware - I’m assuming by now the software/hardware has been updated and no longer running on valves & Cobol?
How on Earth do you test a critical system like that? We used TPNS to simulate millions of ATM transactions taking place along with some real different models of actual ATMs being used non-stop over a period of 72 hours simulating the known peak periods, like the 2 weeks prior to Christmas.
I’m again assuming (because I actually don’t know) that ATC testing used Flight Simulation Software along with some real planes with test pilots that mimicked actual peak periods at major world airports? I certainly hope that they ignored the 83% testing rule and got as close as possible to the unachievable100% as I do actually believe passenger safety supersedes any money systems in terms of priority BUT I think there may be Financial Directors and/or Bean Counters of large Corporations that would think the opposite.
I have to agree on Agile - I have a friend who is an Agile Consultant (is that an Oxymoron?) Contractor who lives and breathes the stuff BUT I’ve always been a bit sceptical of these ‘fly by night’ so called ‘improvements’ to Project Managent especially when it involves phrases like ‘Blue Sky Thinking, Helicopter View(s), circle back, reach out and Morning Scrums. Any Processes or Management Techniques that would have required me to “stick my head up other colleagues bottoms” would have had me racing off to find a new contract!