# Calculate CI for sigma

Six Sigma – iSixSigma Forums Old Forums General Calculate CI for sigma

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• #52663

Ang
Participant

Hellu

I would like to have some suggestions how to calculate CI-level for a sigma value.

Say for example I have done 100 measurements and calculated to Cpk=1,33.

Thats 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

/peteR

0
#185528

Mikel
Member

Do 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.

0
#185530

Ang
Participant

mean: x-bar +/- t*SE
st dve: Sqr(n-1)s^2/ChiSq n-1 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 Cpk-x to Cpk-Y (CI whatever needed). In order to be CI (whatever needed) sure you have to take ## samlels.

This is the part I just cant get together and would be thankful for some advice.

/peteR

0
#185550

Bower Chiel
Participant

Hi Peter
An approximate 95% confidence lower bound for “true” Cpk is given by: –
Cpk-1.64*sqrt(1/(9n)+Cpk*Cpk/(2n-2))
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 39:331-340).  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

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#185569

Ang
Participant

Thanks 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
/peteR

0
#185570

Szentannai
Member

Hi Peter,
if you are interested in the confidence intervals for sigma values (aka z-bench) this is the link:http://www.minitab.com/support/documentation/Answers/CapaNormalFormulasBenchmarkZs.pdfGood luck with it, you’ll need it :)Regards
Sandor

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#185586

Ang
Participant

Thanks! 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 =)

/peteR

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