German Tank Problem - Historical Problem

Historical Problem

In wartime, a key goal of military intelligence is to determine the strength of an enemy force: in World War II, the Western Allies wanted to estimate the number of tanks the Germans had, and approached this in two major ways: conventional intelligence gathering, and statistical estimation. The statistical approach proved to be far more accurate than conventional intelligence methods; the primary reference for the statistical approach is Ruggles & Brodie (1947). In some cases statistical analysis contradicted and substantially improved on conventional intelligence; in others, conventional intelligence and the statistical approach worked together, as in estimation of Panther tank production, discussed below. Estimating production was not the only use of this serial number analysis; it was used to understand German production more generally, including number of factories, relative importance of factories, length of supply chain (based on lag between production and use), changes in production, and use of resources such as rubber.

To estimate the number of tanks produced up to a certain point, the Allies used the serial numbers on tanks. The principal numbers used were gearbox numbers, as these fell in two unbroken sequences. Chassis and engine numbers were also used, though their use were more complicated – various other components were used in the cross-checking of the analysis. Similar analyses were done on tires, which were observed to be sequentially numbered (i.e., 1, 2, 3, …, N).