During World War II, America and her allies needed to estimate the number of Panzer V tanks Germany had produced. The solution was simple: Look at the serial numbers of the captured tanks. If you assume the tanks had been sequentially numbered — as in fact they were — you could view the serial numbers of the captured tanks as random samples from the entire range. You could then use statistics to estimate the range and hence the number of tanks produced. More details available here.
A few years later America tried to use the serial number trick to estimate the number of Soviet strategic bombers. This time the trick backfired.
In 1958, American military intelligence believed the USSR would soon have four hundred Bison and three hundred Bear bombers capable of striking the American heartland. Their evidence was the high serial number of a Bison that had flown at a May Day parade in Moscow. In fact, the Soviets knew the Americans were watching, and intentionally inflated that number. — Rocket Men, page 118.
The Panzer estimate was accurate because the Allies had hundreds of data points, enough to support the assumption that the tanks were sequentially numbered and to make a good estimate of the total number.
The Bison bomber was only one data point, but it was consistent with what intelligence services (wrongly) believed. At that time, the US had grossly over-estimated the military capabilities of the USSR. According to Rocket Men, Khrushchev turned down US offers to cooperate in space exploration because he feared that such cooperation would give the US a more accurate assessment of his country’s military.
Related post: Selection bias and bombers