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Sigma calc for nonnormal distributions

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  • #51562

    JimTreo
    Participant

    Being relatively new to this site and to Six Sigma….this forum has been so helpful to me..!!  Would like to solicit some help….I have nonnormal data…trying to calculate sigma for this data….can someone confirm I did this right.
      (Using minitab)…..I used individual distro identification to confirm distribution…..then used nonnormal capability analysis, inputted the distribution and spec limits……used ppm total to convert to sigma value. 
     

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    #179051

    Savage
    Participant

    If data is not bell-shaped, I would use the same sigma that comes from Excel when you calculate the standard deviation. i.e. =STDEV

    This is sometimes referred to as the standard deviation of the individual values. Anyhow, back to your question. Use this sigma and then calculate your index, Ppk, using a technique like that illustrated on page 142 of AIAG’s Understanding Statistical Process Control Second Edition.

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    #179054

    Ken Feldman
    Participant

    Your response makes absolutely no sense at all!!!!

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    #179055

    Ken Feldman
    Participant

    If you have been on this site a while you will have concluded by now that reporting out sigma level is silly.  From your description it appears that you followed the correct steps in computing the capability analysis for your non normal data.  Since “sigma level” is predicated upon a normal distribution using the ppm from your non normal distribution might not make a lot of sense either.  I hope you weren’t worrying about the 1.5 shift thing.  Why don’t you just stick with the ppm or Cpk/Ppk if you get one.  As an alternative, you could have transformed your data and done a normal capability analysis assuming you have process understanding and that it is what it is and it is non normal.

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    #179056

    JimTreo
    Participant

    Thanks Darth (I read your posts with great interest, you definitely know your stuff and give valuable input)…
    I have done transformations in the past..and worked it in that manner.  But I have always been interested in “knowing” how to run it without transformation of the data. 
    I have heard its probably just as good to treat the nonnormal situation by running it through a discrete sigma calc.  Example: total, how many out of spec, opportunities for defect, etc.  Would be interested in your thoughts around that approach/ treatment?  Is that even a valid approach? 
    PS- I agree with you on the sigma level reporting…but unfortunately, am required to “sigma-tize” my capability in our reportouts. 
     

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    #179057

    Ken Feldman
    Participant

    Thanks for the kind words.  Make sure Carnell knows it!!!
    Discrete measures of capability are OK but you lose quite a bit of knowledge.  You can report it out in addition to providing any Cpk or Ppk numbers.  Although you may be able to fit a distribution to your  current data set in hindsight, that doesn’t guarantee that the true population actually operates as that distribution.  Drawing long term conclusions might be a bit tricky.
    If you want to experience something scary…and I do this in class….use the random number generator for Minitab to generate a bunch of data using your supposed data parameters…depending on the distribution.  Now run your capability study a number of times against your spec.  You may see the capability shift dramatically as a function of the specific random data set.  Often doing a capability study is a snapshot in time and today you are OK and tomorrow you may not be.  In class I do it with normal data which might be the best possible situation.  After setting a base number, we generate 1,000 random values using a specific mean and s.d.  Then each student randomly selects 25 data points from the population and does a capability study using some spec I give them.  Much to everyone’s surprise there are a number of students who are shown to be incapable of meeting specs while others do.  All of this is from the same population.  This easily demonstrates the concept of sampling variation/error and that a snapshot capability as you are doing is merely a crap shoot.
    If your management is requiring that you sigmatize everything then they probably aren’t too sharp so you can probably give them anything and they will be happy.  So, next time your process shows it is not capable, just redo it with a new sample and odds are you will be OK.
     

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    #179070

    JimTreo
    Participant

    Darth..
    Thank you for the clarity..!!  And that is a great exercise you use in class…if you dont mind, I’ll pass that idea to our trainer for “another way” to illustrate that concept..!! 

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    #179072

    Ken Feldman
    Participant

    Be my guest and consider it a gift from Dear Ole Santa Darth.  I gotta a million of those types of teaching tricks.

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    #179077

    Savage
    Participant

    And your reply is supposed to help other readers?
    I made a post to educate at least one person, and if this worked, I am happy. If you do understand my post, you can either ask for clarification or zip it. Didn’t your mother tell you “If you do not have anything nice to say, then don’t say it at all.”

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    #179079

    Ken Feldman
    Participant

    Well, your post wasn’t very helpful.  In a highly skewed distribution, the use of the mean is less than appropriate.  Therefore, the use of the standard deviation as you described is inappropriate.  In fact, if you understood something about non normal distributions, you would realize that the calculation for s.d. is not the same as for a normal distribution which is what you suggested.  Now maybe you can clarify why you suggested the use of a sample standard deviation using a sample mean and based on a normal distribution for someone analyzing non normal data.  Thanks for your insight.

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    #179087

    SS
    Member

    Agree

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    #179094

    Savage
    Participant

    In short I was trying to communicate (very poorly, I suppose) that one technique for dealing with non-normal data is to follow the AIAG manual. 
    One of their techniques calculates the std. dev. the regular way. However, when it comes time to calculate a capability index such as Pp or Ppk, a different technique is used. As I think I remember, the area under the (non-normal) curve is integrated from a distance far beyond where the tails come down until you reach a point where the area under the curve on each end = 1/2 * (1 – 99.73%). This point is then used to see how many std. dev. exist between here and the mean and this number (usually not 3) is used as the denominator in the Ppk calculation. I am doing this from memory, and I probably am making a mistake, so I suggest anyone interested in this approach look at the AIAG and see this alternative approach.

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    #179096

    Ken Feldman
    Participant

    Thanks Matt. Since the poster mentioned he was using Minitab it was just as easy for him to use the non-normal capability function. Once he defines the distribution of best fit…at least for the data set he has….Mini will use the actual distribution parameters to calculate the area beyond the spec of interest.

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