
Re: Failure rate of population of components: Underdamped response to step function
Posted:
Nov 6, 2013 12:24 PM


On Wed, 6 Nov 2013 07:58:24 0800 (PST), paul.domaskis@gmail.com wrote:
[...] me>> >> Depending on how particular you are, you can't just overlay the >> graphs to show "all failures" after the 3rd or 4th failure; you want >> to add the densities. >> >> Clearly, by the time you have reached the time of the 25th failure >> ontheaverage, many devices will be on an earlier or later count, >> because the SD is now 25, and the peak is no longer prominent. > >Rich, I get that if you superpose the t1, t2, etc., you get a series of diminishing peaks. [break]
Okay. That is what I thought you were trying to explain. What you say in further explanation just leaves me puzzling.
It might be that the physical model you have in mind is not one that I am familiar with, or I've just got a block that is preventing me from imagining it. I am lost.
> However, the time to failure of the architypal component is decaying exponential rather than normal. [break]
A Poisson model has exponential decay in timetonextevent. And they are uncorrelated. Poisson posits a constant, fixed, "uniform" rate for events.
Failure rates ordinarily increase with aging. I thought you were describing that sort of model. That seems to be required if you will have any peak for events other than at the start.
> 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."
Are you indeed plotting events?
> >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]"?
 Rich Ulrich

