However, less well known, is that you can further estimate confidence intervals for the total N using the second and subsequent highest serials taken.

You generate likelihoods for each of nth serial holding its observed value, for a suspected total series of N. The binomial can be used to do this easily – what is the pdf that n-1 out of N serials will occur in a series of trials with P(success) = (n/N). The subsequent series of likelihoods for each n can then be summed for every value of N to get its overall distribution.

This gives you a much tighter estimate of N; I haven’t seen the trick commented upon yet, but it seems obvious and doesn’t throw away information.

Tanks were pretty easy–There were only a couple of factories. Small arms? Holy hell, but everyone with a machine shop was producing parts, which would get assembled at different places, seemingly randomly. Friend of mine was a Mauser rifle collector, and if you talked to him about his collection, it didn’t take too long before your eyes would start glazing over as he went over all the little variations. He had a goal to have every single variant of Mauser rifle ever manufactured and issued by the Germans in WWI and WWII, and I think I remember him saying that would be something on the order of a thousand different rifles…