Hello,
I'm haviong a discussion with a customer about calculating CpK and PPM values in case of an underlying Log Normal Distribution. Does someone have the formula at hand or can point me to a source for it?
Thanks
Bernd
Bernd: Won't the Log Normal curve fitting option within the Distribution platform give them everything they need in terms of the Cpk and PPM? I don't honestly know if the underlying formula is contained in the JMP documentation statistical details...
Hi Peter,
yes, the fitted platform gives all information needed. It’s a matter of understanding. It is not easy to explain that if I transform my data and my spec limits and use a normal distribution I get the same sigma quality but completely different CpK values. All quality engineers are trained to interpret CpK values, but if the underlying distribution is not normal, it’s hard for them to understand why they can’t interpret CpK the way they are used to. So I want to explain the calculations a bit better. The formulae are not given in our books, therefore I’m asking.
Hi Bernd,
How about using bootstrapping in Pro to get 99% or other confidence interval for a normal and log-normal to explain the difference. If the goal is to educate via a demo this may be a viable option. Although a stretch, might even get your customer interested in Pro.
Malcolm
Makes perfect sense...I too often had challenges with folks interpreting nonnormal process capability issues to folks. One nonmathematical way in which I tended to have luck with engineers is to get them to think in quantile/ppm terms for the underlying distribution, no matter the shape. Then just kind of do a moral equivalent Cpk calculation in their mind. If there's lots hanging outside the specs, then their Cpk is awful...if there's nothing...it's good. After that who cares about the actual number? It's what you do next that is most important. Most of the engineers I worked with were OK with this sort of logic.
I always encouraged plotting the underlying process data, then using that to give you an eyeball estimate of what's outside the tails...and that will get you close. And from a practical point of view gives you more insight than the Cpk statistic all by it's lonesome.
