W is for . . .

This month I'm posting Mad-Cool-Math Nuggets.


 Image courtesy: rsteup

W is for Wald, as in Abraham Wald and a memo he wrote during WWII about damage to planes that had flown over Germany and returned. The idea for this blog comes from the article Five Statistical Problems That Will Change The Way You See The World from the site Business Insider.

As a member of a statistical research group, Wald's job was to collect data on which parts of a plane were hit the most by German fire. This information was supposed to help determine where the planes might be reinforced. So far, so good?

Now Wald found more bullet or flak damage to the fuselage and fuel systems than to the engines, so guess which parts he recommended to reinforce?

The fuselage and fuel system, right? No! Here's the twist: He was collecting data from planes that had returned, not the ones that were shot down. So Wald reasoned that the fuselage and fuel system could handle serious damage from bullets and return, while the engines could not. In other words, the returned planes showed little damage to the engines because the engines that did sustain serious damage never made it back.

Smart fellow.

This kind of statistical research in WWII was the beginning of Operations Research, which uses techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, to get optimal or near-optimal solutions to complex decision-making problems. (Wikipedia) That was a mouthful, wasn't it?

Here is some information about the plane in the image above from the photographer:

A beautiful C-47 at the 2009 Geneseo, NY air show. This aircraft originally served with the 12th Air Force in the Mediterranean Theater in 1943 and the 9th Air Force in England 1944-1945 as part of the 316th Troop Carrier Group. It was one of the lead aircraft of the first strike of the D-Day invasion on June 6th, 1944. More info at 1941hag.org.

Impressive! Coincidentally, Geneseo is practically next door to where I live, Rochester, NY.

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