On Sun, 10 Nov 2013 10:50:58 -0800 (PST), firstname.lastname@example.org wrote: ... > >I think I should have been clearer about the fact that I'm not trying >to model second order systems. Rather, I'm trying to find a reference >for the failure rate with time of an ensemble of parts with Poisson >failure rates, each of which are replaced upon failure. I assumed >(perhaps wrongly) that it is well-known and iconic, since it shows up >in reliability material that I alluded to in my original post.
I've looked back at your original post. You do mention there, correctly, that there is a curve that becomes asymptotically "Poison" in distribution of failures counted in small time intervals; the failures eventually tend to occur uniformly.
I think you have a serious misunderstanding of the vocabulary, and of the point being made in your source.
EVERY curve with a continuous, increasing failure rate is going to have some a defined MTTF. This is not peculiar to some single failure curve. If you replace every failure as it occurs with a "new" part, the curve is going to be "damped" when you look at later peaks, and the curve is going to evolve toward a uniform rate of failures as the starting points become heterogeneous. It is "uniform rate" that invokes "Poisson" as one of the possible descriptors.