During World War II, the American B17 bomber fleet was suffering heavy losses, on account of all those Luftwaffe pilots who took exception to Americans dropping high explosives on their cities, their families and, potentially, their Führer.
So, the USAF decided that they needed to beef up the B17's armor in order to improve its survivability. Trouble is, unlike the knights of old, you can't just encase an airplane in cast iron. It (the cast iron) tends to weigh a lot, which negates the aircraft's ability to, you know, fly. So additional armor had to be applied sparingly, in strategic places.
The next obvious problem was, how to identify where those "strategic places" were. Simple. In order to figure out where the returning bombers are taking the most battle damage, you start keeping detailed records of where on the aircraft you're seeing the most bullet holes. Those, surely, are the areas that need additional armor protection. Makes sense, right?
"Wrong", said a mathematician by the name of Abraham Wald. You want to figure out those places on the aircraft where you never, ever see any bullet holes. Those are the areas you want to better protect. Why? Because the bombers that you're examining did return from their missions, in spite of being bullet-riddled. The ones that you want to worry about are the ones that don't make it back; the ones whose bullet holes you never get to inspect. So it follows that, if there are areas where you never see bullet holes, it's not so much because no bombers ever get hit there; rather it's probably because the ones that do get hit there don't come home.
And so it was that additional armor was applied to parts of the B17 that never, or almost never, seemed to show any battle damage, such as certain angles of the cockpit or at the base of the vertical stabilizer. And in so doing, countless bombers and their crews were likely saved.
Hats off to Abraham Wald. Now that's thinking outside of the box!
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