On Fri, 15 Nov 2013 15:59:35 -0800 (PST), email@example.com wrote:
> ru>> >> 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.
I would say that the population can be described by (or as) a Poisson process, and I think other biostatisticians would, too. Maybe some specialties use the language you suggest, but it seems more proper, to me, to say something like "constant hazard", etc.
Still. "constant failure rate" implies NO PEAK. That is the situation at the asymptote, in the picture you linked. It is not the situation that creates a peak.
> Actually, it also >implies exponentially decaying PDF for time-to-failure. Again, sorry >for not being more specific.
That would be, "exponentially decaying time-to-NEXT-failure" for the population. Uniform distribution. Poisson. These are intimately related.
> >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.