Paul
Posts:
359
Registered:
2/23/10


Re: Failure rate of population of components: Underdamped response to step function
Posted:
Nov 7, 2013 11:57 AM


Sorry, but I left out a crucial detail when I started this thread. I'm not just referring to a population of parts. I'm taking about a population of parts that are replaced upon failing. Makes a big difference, I know.
On Wednesday, November 6, 2013 12:24:16 PM UTC5, Rich Ulrich wrote: >I wrote: >> So the fact that the 2nd order response to a step function starts >> at zero with zero slope was a bit of a mystery. > > I have no idea what "step function" you have in mind, or what you > mean by "2nd order response."
http://hydraulicspneumatics.com/sitefiles/hydraulicspneumatics.com/files/uploads/2008/02/2008.06Motion2.png
Check out the curve for zeta (squiggle) = 0.25. It's not exactly like that, but that's sort of the idea. Initially zero value and zero slope, accelerates up to a peak at t=MTBF, then oscillates in a decaying fashion. (I tried to shorten the URL, but our site firewall is aggressive and TinyURL isn't considered harmlesslooking enough).
> Are you indeed plotting events?
No, population failure rate.
>> I confided with a colleague, who didn't have a reference. However, >> he described that it is related to conditional probabilities (if I >> understood correctly) which to me means Bayes or Total Probability >> Law. I have yet to sit down and suss it out, but he indicated that >> one has to convolve t1, t2, t3, etc., where they are decaying >> exponential PDFs. I'll chime in if I get to that point. As a >> citation reference, I'm going to cite the manuals where I found the >> curves in (for now). > > The PDF of what ... is "decaying exponential[ly]"?
The PDF for the MTBF of a part is a decaying exponential. Basically, Poisson governed failure.

