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Topic: Failure rate of population of components: Underdamped response to
step function

Replies: 15   Last Post: Nov 18, 2013 10:15 AM

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Paul

Posts: 263
Registered: 2/23/10
Re: Failure rate of population of components: Underdamped response to
step function

Posted: Nov 7, 2013 11:57 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 UTC-5, 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/site-files/hydraulicspneumatics.com/files/uploads/2008/02/2008.06-Motion2.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 harmless-looking 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.


Date Subject Author
11/4/13
Read Failure rate of population of components: Underdamped response to
step function
Paul
11/4/13
Read Re: Failure rate of population of components: Underdamped response to step function
Richard Ulrich
11/5/13
Read Re: Failure rate of population of components: Underdamped response to
step function
Paul
11/5/13
Read Re: Failure rate of population of components: Underdamped response to step function
Richard Ulrich
11/6/13
Read Re: Failure rate of population of components: Underdamped response to
step function
Paul
11/6/13
Read Re: Failure rate of population of components: Underdamped response to step function
Richard Ulrich
11/7/13
Read Re: Failure rate of population of components: Underdamped response to
step function
Paul
11/7/13
Read Re: Failure rate of population of components: Underdamped response to step function
Richard Ulrich
11/10/13
Read Re: Failure rate of population of components: Underdamped response to
step function
Paul
11/11/13
Read Re: Failure rate of population of components: Underdamped response to step function
Richard Ulrich
11/15/13
Read Re: Failure rate of population of components: Underdamped response to
step function
mr.fred.ma@gmail.com
11/15/13
Read Re: Failure rate of population of components: Underdamped response to step function
Richard Ulrich
11/15/13
Read Re: Failure rate of population of components: Underdamped response to
step function
Paul
11/17/13
Read Re: Failure rate of population of components: Underdamped response to step function
Richard Ulrich
11/18/13
Read Re: Failure rate of population of components: Underdamped response to
step function
Paul
11/5/13
Read Re: Failure rate of population of components: Underdamped response to
step function
Dan Heyman

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