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Statistical Techniques and 6 Sigma Cpk for one sided dimension

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Author  Topic: Cpk for one sided dimension 
dave@utah unregistered 
posted 28 January 2000 06:24 PM
What is the formula (or concept) for calculating a Cpk on a "smaller is better" dimension. Specifically, I am trying to calc Cpk for a GD&T true position of .030. And would the same concept work for profiles, flatness, runout, etc. Thanks Dave IP: Logged 
Don Winton Forum Contributor Posts: 498 
posted 31 January 2000 07:07 PM
Go to /pdf_files and download CPK.PDF. That should explain all you need. IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 22 March 2000 08:31 PM
Some additional 'thought food': >Luiz Alberto Rodrigues wrote in message  From: "Kevin Terrill" Luiz, I'm sorry Luiz, but I am as dumb founded as you are at this. Can any Statismajicians please explain? 99.73% is arrived through a normal bilateral distribution, given a +/ 3 sigma dist.. The part that is not inside the +/ 3 sigma is 0.27%. I can see were the 0.135% came from, its just that I cannot justify it. If I put the outside of the normal curve on zero, the smallest sigma value would still be 0.135% of the total range away, and the max sigame value would be at 99.865% away, but this would still leave 0.27% of the curve outside of the +/ 3 sigma range. Luiz, could you explain who told you this? Thank you, Kevin Terrill  From: BML bmlank@mydeja.com The problem with the onesided Cp/Cpk etc. is the fact that it does not take into account the other side. For example, you state that even for a unilateral measurment, 0.27% is still outside the +/ 3S limits. That is true. However, since the measurement is unilateral, we're not concerned with one of the tails, so it doesn't count. (Remember hypothesis testing?) The tolerance is unilateral exactly because that other tail doesn't count, i.e. the part is good even if it is in that one tail. Therefore the only way you can have a bad part is if you are in the *other* tail, which has an area of 0.27/2 = 0.135. Kinda confusing, but that's the way it works. Ben  From: "John Duffus" jduffus@wwonline.com Here's another way of looking at it. You are running a marginal process with a Cpk of one, i.e with .00135 fraction defective in each tail for a total of .0027. The specification is then changed so that one tolerance limit is disregarded, So you can now say, good, now I only have .00135 fraction defective. You improved the fraction defective, not by having a better process but by relaxing the tolerance. If you start from an objective of a certain fraction defective, you could argue that you should have a lower Cpk for a onesided tolerance, but if you put all your fraction defective in one tail you have an increased sensitivity of the fraction defective to shifts in the process average. In any event fraction defective depends on an assumption of a normally distributed population making the calculations only very approximate in most cases. John Duffus IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 29 March 2000 08:35 AM
Tomo Doran tomodoran@aol.com misc.industry.quality Re: Capability The whole argument about unilateral characteristics and their meaning in reality is often wrongly interpreted in industry. Firstly, for a process with a natural boundary (such as flatness) of zero and a upper tolerance the model distribution when the system is tuned to peak performance (centred) and has no external variation is  Rayleigh Distribution. However, this very seldom happens in reality. The secret of successful capability studies are to ignore what distribution model it should be {afterall, the process doesn't care what you 'think' it is} and concentrate on modelling the actual data. This model can then be used to get more realistic capability assessments of the process. In order to do this you need a statistical analysis software that can do this. I recommend the package I use  qsSTAT by QDAS. I have used this many times to the advantage of machine tool builders to rationalize just situations. Email me back for further information IP: Logged 
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