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Normal Distribution?

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  • #32543

    Hogg
    Participant

    If the measured attribute is not in a normal distribution, can six sigma techniques be used?

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    #87045

    Ryan
    Member

    Yes, because it’s in relation to your specification limits.

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    #87049

    Zilgo
    Member

    Not so fast, my friend.  Most of the statistical analysis done in six sigma relies on the assumption that your data set is normal.  Too many times people bring stuff across my desk and say that their results are good but when I check the assumptions of the tests they ran, they ignored the fact that their data is non-normal.  They are about a million threads on this site that discuss what to do when you don’t have normal data.  You can still apply six sigma techniques, but you have to pay better attention to the statistics and make sure you don’t violate any assumptions.

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    #87050

    faceman888
    Participant

    I agree with Zilgo.  You probably won’t be able to apply the ‘classic’ methods taught in most 6 six sigma courses.  The bulk assume normality.  However, there are methods that don’t assume normality that do the same things as the ‘classic’ methods.  You can test for independance, differences between measures of central tendency, etc.  In a pinch you can do transformations also.  Definitely don’t rule out a project just because your measureable isn’t normally distrubuted.

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    #87054

    MMBB
    Participant

    I tend to fall on the opposite opinion – most of the Six Sigma tools are quite robust against non-normality, so long as your sample sizes are sufficiently large.
    The only place normality is really important is process capability and control charts, and even then, many feel they are fairly robust. Obviously both techniques have methods that provide non-normal alternatives (transformation, use of other distributions).
    I suppose some of the variance component methods, including GR&R, have an assumption of normality that is fairly important.

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    #87057

    Hmm…
    Participant

    I tend to disagree, specifically from an SPC and process capability point of view. 
    First things first though…is the data supposed to truly represent normality (Guassian distribution), or are you looking to justify approximate normality?
    One question that comes to mind is this: If the data is truly non-normal and is supposed to represent normality, and process stability cannot be determined, then how do you truly know how to improve the process?  One of the foundations of SPC that is paramount to any process improvement is that one should truly know what they are dealing with before trying to improve the process.  Plus, how can someone truly measure process capability or performance if the process is truly unstable?  If these cannot be determined, then you might accidentally end up “spitting in the wind.”
    True, transformation could help, but within my limited experience, I’ve found that non-normal data that is transformed according to accredited statistical techniques, unfortunately ends up non-normal as well.  This does depend on the data that you are working with though.  Although, there are always exceptions.  As well, to quote a pioneer of Project Management, “Bad data is usually better than no data.”  Therefore, I’m a firm believer that anything is possible!
    One recommendation though:  can the variation be streamlined to ensure stability…i.e., are there outliers or special causations that can be identified and controlled?  If so, then bringing the process into control can ensure that you have a clear picture of what you are dealing with.
    None-the-less, sounds like fun!
    Things that make you go hmmm….?

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    #87059

    Hogg
    Participant

    My (limited) understanding of sixsigma is that sigma means standard deviations. That we are aiming to have failures in the tail represented by that portion under a distribution graph which lies at least 6 sd’s from the mean.
    This assumes several things: that the distribution is normal. That there is a distribution. (a measured variable), that there is a mean.
    If dealing with a yes/no situation, pass fail say, then this is not a distribution. There’s no mean. (Unless we group batches of data.)
    So for situations where there is no distribution, therefore no mean, and therefore not a normal distribution, the word sigma seems to become meaningless, and to use the technique inappropriate.
    To be more specific. I have a business where the main quality criteria are not measured variables, but pass fail type tests. There are variable numbers of units in an order (rarely the same), from 1 to 500 or so. Orders a day average about 30-40. Three main quality tests look for a specific attribute, which if present means a failure of that piece within that order. (If the order had only one piece, the whole order fails).
    So, from the tests I don’t have a number, a value, of some measured variable, I have a pass or fail. I do have an objective, and that is zero failures.
    Now 6 sigma techniques say I should just define the defect, the units, and the opportunities. Sounds simple, and applicable to this situation. But my question is: When the underlying assumptions of six sigma are not considered (normality, distribution, mean, sd’s etc), are we in danger f applying an inappropriate technique. If we don’t consider the assumptions, we don’t test them. And failure to test them and adhere to them might make the outcome erroneous. And we might unwittingly lead ourselves astray.
    Anyone help me get on track?
     

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    #87061

    Amoore
    Participant

    No, this is a binomial distribution, but plot the number of defectives per sample against the number of samples and treat this is a normal distribution.  Statistics by F owen and R Jones will help explain details.

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    #87069

    Ron
    Member

    Absolutely,
     
    Some organizations are way to anal about normal data. Normalacy is not even an issue for control charts. The only area of concern is some of the hypothesis testing tools.
     
     

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    #87072

    faceman888
    Participant

    Geoff,
    Don’t take the ‘sigma’ in six sigma too literally.  You are correct in that sigma can be synonymous with standard deviation.  However, it is frequent in six sigma implementations that the term is generalized to be a measure of process performance independant of what type of data your measureable is.  In your case, pass / fail data, sometimes referred to as discrete or binomial more specifically, you would take your proportion defective and go backwards through a z table (or let a stats program do it for you) to determine the ‘sigma level’ or Z score of your process.
    Your data probably does have a distribution.  It is probably binomial.  If you counted the number of defects on each unit instead of categorizing each unit as pass or fail it would probably follow a Poisson distribution.  The mean in your case would be the number of failed pieces divided by the total number of pieces.  This is your proportion defective.
    There are many six sigma methods that apply to binomial data.  Tests of two proportions, generalized linear models, are few.  There are a bunch more.
    Think of sis sigma more as a process for improving processes that is disciplined and sequential in nature not as a specific measure of dispersion.  The six sigma process includes various steps, each step with an intent.  You can plug in whatever valid statistical methodolgy is required to meet the intent of the step in six sigma and the type of data you are dealing with.  A lot of BBs do a lot of defective or defect type projects.
    Good luck.

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    #87073

    faceman888
    Participant

    MMBB,
    You are right.  Many six sigma methods are fairly robust against non-normality.  However, in Geoff’s case, the data is binomial.  I would suggest that it would be better to use methods specific to binomial ditributions instead of relying on the ‘robustness’ of methods that assume normality.  There are a bunch of methods for binomial data that do the same thing as their ‘normal’ counterpoints. 
    I agree that when you can’t characterize data as some other known distribution and you have mild deviance from normality that most ‘normal’ methods will hold up.

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    #87079

    KBower
    Participant

    You raise some interesting points.  Regarding the assumption of normality, I’ve a paper on “Some Misconceptions about the Normal Distribution” reprinted (with permission) from another Six Sigma oriented site.  You may access it (for free) via
    http://www.minitab.com/company/virtualpressroom/Articles/StatisticsArticles.htm
    There’s also another paper that discusses the robustness of the 2 sample t-test to normality (via an argument involving randomization procedures).  That paper is “The Two-Sample t-Test and Randomization Test” – also available at http://www.minitab.com/company/virtualpressroom/Articles/StatisticsArticles.htm
     
    Hope this helps.
    -Keith

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    #142366

    Ang
    Participant

    Zilgo,
    Wonderful to see someone on this forum who knows what he’s talking about.

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    #142374

    Ken Feldman
    Participant

    Peter, Zilgo posted that over 3 years ago and hasn’t posted anything since.  Plus he now believes that the 1.5 shift should really have been 1.79 because Harry forgot to account for the fact that the distribution was Chi Square.

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    #142380

    Ang
    Participant

    Darth,
    We both look like idiots now that Mikel Harry has admitted he made an error with the 1.5 shift. 

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    #142384

    Ken Feldman
    Participant

    And you are actually gullible enough to believe that Mikel Harry would fess up on this Forum?????  Gotta get some of whatever you’re smoking!!!!

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    #142385

    Ang
    Participant

    Darth,
    It sounds as though you know Mikel Harry and have heard him “fess up” in private.
    God bless

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