Plackett-Burman designs

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    Jack W

    Do you have any experience using  Plackett-Burman designs? We had been thinking on using it, but results interpretation seems to be quite difficult. Any comment is welcome,


    Mike Carnell

    You need a reason even if it is just because you want to try it. For most, you determine what you want to know and select the best tool to get you there.
    This is why I like Bob Launsby’s book “Straight Talk on Designing Experiments.” He doesn’t take the position of a Classical design, Taguchi design, or whatever is the answer to every problem. He mixes them and discusses them without prejudice. Bob has software as well but I think it is separate from the book. You might try it as a reference.
    I have had a BB candidate who came from a particular consulting firm that seems to be dedicated to the advancement of the use of PB designs. While most everyone else completed their Improve phase in the alloted 4 weeks, this person spent 6. That may or may not have been a function of the person. In the end they got an answer just like everyone else. Instead of teaching everyone that they had a better way they really shut down anyone else trying it.
    Just pick the right tool for the job. Nothing is particularly difficult to analize any more with software and I am pretty sure Minitab does PB designs.
    Good luck.



    For what it’s worth the PB is a powerful tool, but you do pay a price for using it.  You end up confounding a lot of variables together and it is a little confusing to grasp.  If you need a powerful screening design to knock out some variables then this would be a good way to go.  My suggestion is though if you can knock out several of the variables now you may be better off sticking with the 2^k and getting more bang for the buck.



    The only legitimate use of PB or saturated Taguchi designs is screening. You would never use them for modeling.


    Robert Butler

      Plackett-Burman designs, like highly fractionated 2 level factorial designs, are for screening a large number of factors in order to identify the “big hitters” – the main effect variables that have the biggest effect on your process.
      Fractionated 2 level designs are always 2 to some power. Plackett-Burman designs are based on multiples of 4.  Thus, 2 level designs increase as 4, 8, 16, 32, 64, 128, while Plackett-Burman designs go as 4, 8, 12, 16, 20, etc.  This means that if you are interested in checking out, say, 11 factors the minimum traditional 2 level design that you could build would have 16 experiments whereas the Plackett-Burman would have only 12.
      If you have adequate statistical software to permit a proper analysis of the design the analysis and interpretation of Plackett-Burman results should be no more difficult than when analyzing any other kind of screening design.
      Because it is a main effects design you will have no information concerning interactions or curvilinear behavior. Consequently, the resulting models should be used as a guide for further work and not as a final model for purposes of process control. 
      If all of the variables of interest are quantitative and the design space is such that you can have three distinct levels for each variable then one way to maximize your results and minimize your efforts would be to set up the P-B design and add a center point and run the replicate on the center point alone.  The residual analysis of such a combination will give you a clear indication of the presence of curvilinear effects in your process.  You won’t know which variable (or variables) is responsible but you will know that the effect is present and must be identified before you can claim to have an adequate model of your process.
      Before you decide to go ahead with a P-B design I can only echo what others have posted to this thread-don’t just pick a design and run it.  First consider what you want to do and then let your wants guide you in your design choice.  If your wants are such that none of the “look-up” designs meet your needs, you will need to seek the guidance of your local statistician.



    For situations with 3-4 input variables, a full factorial is the economical answer.  When you get to 5 inputs, half fractionals become attractive.  At 6 or more inputs, P-B designs can be the best alternative.
    The best approach that I have seen is in Wheeler’s Understanding Industrial Experimentation.  He takes an approach that is different from Minitab, and which I like a lot better.
    With proper handling, a 1/16 fractional P-B can give you a very decent model for all main effects and two-way interactions, without a huge amount of work.  Sometimes the model produced is quite adequate, and other times you’re going to want to run a confirmatory full factorial on the active variables.
    I have a little spreadsheet that takes care of the P-B calculations.  You have to do the scree plot manually, but the spreadsheet does let you follow the Wheeler approach fairly easily.  If you want a copy, email me at [email protected]

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