An airplane, as opposed to, for example, a website, is a system where any failure in certain systems is completely unacceptable, since errors in e.g. flight monitoring can cause the autopilot to malfunction and do a dive. Obviously, this doesn't happen since the brilliant engineers at Boeing and Airbus have checks in the autopilot to make sure it doesn't suddenly decide a dive is a perfectly acceptable and safe maneuver. Or perhaps the computer crashes, and the pilots in the newer fly-by-wire aircraft can no longer actually fly the plane. Of course, there are various safety procedures and redundancies built into these systems to prevent a crash (of both the software and the aircraft).
However, on the other hand, it's quite obvious that software isn't perfect—both open source and closed source software do crash regularly, and only the simplest "Hello World" program doesn't fail. How can the engineers who design the software systems in the aeronautic, medical, and other life-or-death industries manage to test their software so that it doesn't fail (and if it does fail, at least fail gracefully)?
I'm desperately hoping that you're not all going to go: "Oh, I work for Boeing/Airbus/(some other company) and it's not! Have fun on your next flight/hospital visit."