German tanks in WW2

In World War 2, the Allies used statistical methods to estimate German military strengths. For example, to determine how many tanks the Germans had in 1943, the Allied Economic Warfare Division in London analysed the serial numbers on captured German tanks. In the simplest form, each serial number gives information—a serial number of, say, 117 means there were at least that many tanks manufactured.

Using similar but more sophisticated statistical methods, statisticians working for the Allies made the estimates shown in the table below. Allied intelligence agencies were also making estimates based on other information, and these are shown too. All data are monthly production values.

In this case the actual numbers became known from the Speer Ministry after the German surrender, so the true values are known and shown in the table too. The statistical methods gave much better results.

Reference:

Ruggles, R., and Brodie H. (1947) An empirical intelligence in World War 2. Journal of the American Statistical Association, 42:72-91.