Calculate CI for sigma
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 This topic has 6 replies, 4 voices, and was last updated 12 years, 4 months ago by Ang.

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September 18, 2009 at 6:44 am #52663
Hellu
I would like to have some suggestions how to calculate CIlevel for a sigma value.
Say for example I have done 100 measurements and calculated to Cpk=1,33.
Thats fine, Cpk=1,33, but +/ what for CI 95%?
I know there is a function in MTB Process Capability graph to do it, but how is it done manually?
Regards
/peteR0September 18, 2009 at 10:32 am #185528Do you know how to do CI for mean and standard deviation?Those are the only stats in use. Figure it out, it’s not hard.
0September 18, 2009 at 11:16 am #185530mean: xbar +/ t*SE
st dve: Sqr(n1)s^2/ChiSq n1 alph ..
Let me rephrase the question.
What I am trying to do are how to calculate a samplesize to get a desired sigma level. (assuming data is normal distributed) .
The thing I need to prove (preferably in a pedagogic way ;)) to the designers here are:
Yes your calculation tells you Cpk are 1,45 and that are more then Cpk 1,33 that are the demand.
However you only did 5 samples so it might be Cpkx to CpkY (CI whatever needed). In order to be CI (whatever needed) sure you have to take ## samlels.
This is the part I just cant get together and would be thankful for some advice.
/peteR0September 19, 2009 at 8:51 pm #185550
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.Hi Peter
An approximate 95% confidence lower bound for “true” Cpk is given by: –
Cpk1.64*sqrt(1/(9n)+Cpk*Cpk/(2n2))
where Cpk is the estimate from your sample of n data values. This formula is given on page 197 of Thomas P Ryan’s book Statistical Methods for Quality Improvement (Wiley & Sons 2000). It was developed by AF Bissell and published in 1990 in a paper entitled “How reliable is your capability index?” (Applied Statistics 39:331340). If you got an estimate of Cpk of 1.45 from a sample of n = 5 then the above formula gives 0.57. Thus on the basis of the sample you can be 95% confident that the true Cpk is at least 0.57. If you play around with the formula, keeping Cpk with value 1.45, you’ll find that for the 95% confidence lower bound to be 1.33 you would need a sample size of over 200. The theory behind the formula requires the variable of interest to be normally distributed.
Best Wishes
Bower Chiel
0September 21, 2009 at 11:40 am #185569Thanks alot!
This may be very helpful, I will play around with the formula to se if I can use it right of or juse calculate a few exampel.
Regards
/peteR0September 21, 2009 at 11:48 am #185570Hi Peter,
if you are interested in the confidence intervals for sigma values (aka zbench) this is the link:http://www.minitab.com/support/documentation/Answers/CapaNormalFormulasBenchmarkZs.pdfGood luck with it, you’ll need it :)Regards
Sandor0September 22, 2009 at 4:24 am #185586Thanks! Just what I needed (the good luck that is ;))
I will se if I can get a moment of quality time I, the paper and a 12 year old whisky (+my new found luck) this weekend and figure it out ;)
Thanks a lot =)
/peteR0 
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