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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

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    #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.

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    #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

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    #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

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    #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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