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DOE in process with autocorrelation

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  • #32626

    Gaussian
    Participant

    Hello Collegues:
    I want to perform a DOE in a  injection moulding process, but in the mesure phase I’ve find that the process shows a stong autocorrelation, with a sinusoidal shape (like armonic motion) and the estability test fails (more than 9 points in a row on the same side of center line, six points in a row all decreasing, point more than 3 sigmas from center line). This behaviour seems to be normal in this process because we have modified the conditions and the autocorrelation remains in some of the measured dimensions on the part.
    My question is, can I continue the Six Sigma project assuming this behaviour and calculating the needed sample size for DOE as ussual? or must I try to achieve estability before passing to Analize phase?
    Thanks in advance.

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    #87352

    Robert Butler
    Participant

      
      As long as you set up your design and run real replicates of your experimental conditions, the autocorrelation that you see at a given condition over time should not be a problem.  All that the autocorrelation is telling you is that you cannot treat successive measurements at a given condition as independent.  In a design you set up a condition, take a measurement, set up another randomly chosen condition and take another measurement.  Those two measurements will be separated by settings and by times and won’t exhibit autocorrelation. 
      While you didn’t specifically state this, I’m assuming that what you were thinking of doing was taking multiple measurements at a given condition in order to have more than one sample for that condition.  Measurements taken in this fashion will exhibit autocorrelation. This kind of data is called repeat measures.  There are a number of ways of handling data of this type.
      If you don’t have any other resources at your command you can analyze the results of your design by randomly choosing one of your multiple measurements taken at each design point and using the value of that choice as the results of that experimental combination.  Another possibility is to average the results of the multiple measurements, and run the analysis on the averages.  Each of these approaches has its drawbacks. 
      The best way to deal with the data is to use repeat measures analysis.  The problem here is one of computer package complexity and the level of your analytical skills.  Just because you have a package that claims it can handle repeat measures does not mean that it is capable of analyzing DOE’s with repeat measure input.  If your package can handle data of this type you will have to spend some time learning how to properly input your data and how to understand the resultant output.
      What you most definitely should not do is try to treat sequential measurements made at a given condition as replicates.  If you do your computer program will treat this measurement-to-measurement variation as the estimate of error.  It will then use this value to test for significant effects.  Since the data will be autocorrelated, the error estimate will be very small and you will come to the conclusion that many variables are significant when in fact they are not.

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    #87354

    faceman888
    Participant

    Robert,
    Can you recommend a good reference on handling repeats?  There is a lot out there on replicates, and I have read a little on repeats.  I do a lot of repeated measurement designs and would like to upgrade my skills.
    Thanks in advance,
    Faceman

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    #87361

    Robert Butler
    Participant

      The books that I have used for repeated measures are:
      Analysis of Repeated Measures – Crowder and Hand – Chapman & Hall – Monographs on Statistics and Applied Probability #41
      The version I own, in addition to discussing the issues of repeated measures, also has an overview of the software that was available at the time of printing (1993).  The problem is that software changes and unless a revised edition has been published the book makes no mention of SAS Proc Mixed which is my tool of choice when working with repeated measures.
    The second book is
    Analysis of Messy Data Volume 1: Designed Experiments – Milliken and Johnson – Chapman and Hall – 1992
      While it is a book on all aspects of design it does have some very good discussion about repeat measure designs and their analysis.
      Back in 1998 I attended a 3 day course given by the University of Florida on Analysis of Repeated Measures and Longitudinal Data. The instructors were Jane Pendergast and Ramon Littell.  If they are still at the university it might be worth your while to contact them to see if they know of any more recent references.

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    #91035

    Verity
    Member

    Robert,
    I’ve been reading old threads and hope you may be able to help me with a DOE problem.
    I’m doing experiments in injection moulding where the response is usually the strength of a part (destructive testing). I’ve been taking 10 samples (repeated measures) for each run and using the average of these as the response in the analysis – is this correct?
    Also having difficulty identifying significant factors – there is a lot of variation in the parts at each setting and not a huge amount of variation between settings. Have I missed a critical factor, or not set my levels far enough apart, or is my measurment system to blame? Being destructive testing I am having trouble with doing a Gage R&R.
    Verity

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    #91266

    Kim Niles
    Participant

    Dear Verity:
    Injection molded part strength factors that really stand out are related to creating splay or weld lines.  Both of these can be optimized and may appear to come and go depending on what you have in control.  Splay is more related to moisture in your mix.  Weld lines are more related to cold fronts coming together.  Make sure you cover those two somewhere in your study.  You also might want to review my article on DOE as I saw your other posts that it addresses.   See https://www.isixsigma.com/library/content/c030616a.asp and good luck.     
    Sincerely,
    KN – https://www.isixsigma.com/library/bio/kniles.asp  – http://www.KimNiles.com

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