On Friday, November 15, 2013 1:29:26 PM UTC-5, Rich Ulrich wrote: >This shows me your problem: "And specifically, the parts' failure >follows a Poisson process." > > In general, in the real world, the expected failure for one part is > never Poisson. Poisson is a discrete distribution, so you might say > that it is not even a candidate for describing what curve it is that > failures follow for a part. > > Yes, Poisson can describe what is observed when the observed > failures (eventually?) occur at a uniform rate. > > With proper parameterization, it is probably an example of the > Central Limit Theorem. "Uniform" is where you end up when you > average together a large number of starting points. > > > Read what I wrote before -- if you instantly replace every failure, > then the curve of "failures" will flatten out, becoming uniform as > the starting points become heterogeneous. That is true as a pretty > wide generality, if it is not universally true. > > Poisson is the end, regardless of where you start. If you are > seeking an example of something being damped, you need to start out > with something that *has* a peak to be damped. > > Given all that: Do you still have a question?
I think I should have clarified that I mean a Poisson process. My understanding is that it can describe an individual part because it just means constant failure rate or MTTF rather than the infant mortality or wearout extremes of the bathtub curve. Actually, it also implies exponentially decaying PDF for time-to-failure. Again, sorry for not being more specific.
Also, I intuitively agree with what you wrote before about flattening oscillations (if I understood correctly). I was hoping to find a [ maybe intuitive :) ] derivation of it for an ensemble of identical parts. I also suspect that relationships with the Central Limit Theorem can readily be drawn. I intuitively understand what one should expect based on the CLT, though I think the time dimension of the curve that I'm seeking a derivation for makes it more complicated.