Calculating DPMO for Exponential Distributions

T

TickTax

#1
I would be grateful for help with the following problem.

I know how to calculate DPMO for a Normally distributed process, but how do I calculate DPMO for an exponential distribution?

What DPMO figures do 3sigma, 4sigma, 5sigma and 6sigma processes produce?
 
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R

Rick Goodson

#3
I don't have a clue either but will take a look in some of my stat books. I am curious though, why do you need DPMO for an exponential distribution? What is the process your are trying to measure?
 
L

Laura M

#4
It's late and its been a long day. But I'm thinking its the area under the curve from the point (spec limit?) to infinity. Which is the integral, isn't it?

Old brain cells are getting stirred up, but I once did the probability of getting a part out of a "leak spec." Leak distributions are typically exponential. Lots of 0's, and low values, a few creeping up to the spec. I was able to superimposed an "e to the x" distribution over real data. Then from the upper spec forward is the probability, convert to PPM. I excluded "major failures" because we were looking for those that were borderline and subject to measurement error.

I probably should have consulted books rather than shooting from the hip on this one, but you guys that did can correct me!

Laura
 
T

TickTax

#5
Thanks to those of you who have responded so far.

Perhaps I should explain my problem a little more. I'm looking at a queuing process which has an exponential p.d.f. I am aware that for an exponential process with p.d.f lamda*exp(-lambta*t) the mean is 1/lambda and the variance is 1/(lambda^2) If I integrate from 4 sigma(mean plus 3sigma) to infinity (a 3sigma process?) I get 18316 DPMO. Other DPMO's calculated this way are as follows:

4 sigma - 6738
5 sigma - 2479
6 sigma - 912

However, Motorola's DPMO figures assume a mean which drifts +- 1.5 sigma. What I would like to be able to do is to calculate the figures assuming a similar drift in the mean of my exponential distribution.
 
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