Examine your assumptions

by Douglas_Reay 8y30th Mar 201214 comments


There's a story you've probably heard:

During World War II, the British RAF's Bomber Command wanted a survey done on the effectiveness of their aircraft armouring.  This was carried out by inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German air defences was noted and the recommendation was given that armour be added in the most heavily damaged areas.

However a new group, run by Patrick Blackett, the Operational Research Section, analysed the survey report, and came to a different conclusion.   Blackett suggested that, instead, the armour be placed in the areas which were completely untouched by damage in the bombers which returned.   He reasoned that the survey was biased, since it only included aircraft that returned to Britain. The untouched areas of returning aircraft were probably vital areas, which, if hit, would result in the loss of the aircraft.


It is a useful fable, but in the context presented it seemed unlikely, given the attitudes of Bomber Harris.  So I went looking for further information, and found the story of BC-ORS written by Freeman Dyson:

"A Failure of Intelligence" (Part 1) (Part 2)

which is a great read, but fails to mention any such incident.

What I did find, however, on further searching, was the work of Abraham Wald.   Wald was a Jewish mathematician from Romania who in 1943 published a series of 8 memoranda via the Statistical Research Group at Columbia University while working for the National Defense Research Committee in America.  These were republished collectively in 1980 as "'A Method of Estimating Plane Vulnerability Based on Damage of Survivors." by the Center for Naval Analyses, and are still in use today.

In 1984 Mangel and Samaniego published a fairly accessible summary of Wald's work in the Journal of the American Statistical Association (Vol 79, Issue 286, June)

"Abraham Wald's Work on Aircraft Survivability"


So it seems that Wald is the one who should get the credit for being the first to try to compensate for the evidential problem.  Tragically he himself died in an airplane crash, just a few years later (in 1950, aged 48).

The 'bible' on this topic, Robert Ball's "The Fundamentals of Aircraft Combat Survivability Analysis and Design" confirms the problem is a real one, and mentioned the F-4 as an example.  When they looked at the F-4s which survived combat, there were no holes in the narrowest part of the tail, just forward of the horizontal stabilizers. They figured out that all of the hydraulic lines for the elevators and rudder were tightly clustered in there, so that a single hit could damage all of them at once, leaving the plane uncontrollable. The solution in that case was, rather than increasing the armour, to spread the redundant lines out to reduce the chances of losing all of them to a single hit.