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4 factors, 8 runs. Fractional Factorial Design or Plackett-Burman?

Discussion in 'DOE - Design of Experiments' started by Marcel, Mar 19, 2019.

  1. Marcel

    Marcel New Member

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    Hello everyone,

    My colleague did a design with 4 factors and 8 runs and said its a Plackett-Burman Design with resolution III.

    A picture of his design is attached.

    I read a little bit about DoE now and in my opinion its a resolution IV design and I would call it rather a Fractional Factorial Design than a Plackett Burman design. Am I right or is he right?

    Thanks,
    Marcel
     

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  2. Miner

    Miner Moderator Staff Member

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    This design appears to have been randomized, and is nearly impossible to tell. Can you provide the design in the standard order with the columns in the standard design sequence?

    I attached a Plackett-Burman design in standard order. The fact that the design you provided has 7 columns of which only 4 were used is a strong indicator that it probably is either a PB design or a Taguchi design. Fractional factorial design do not typically show unused columns.

    PB8.png
     
    Last edited: Mar 19, 2019
  3. Marcel

    Marcel New Member

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    Thanks for the quick answer!

    1.) Unfortunately, I only have this table. Is this design really randomized? Because for each row the signs are moved one position to the left. I thought, this is how you create a Plackett-Burman design.

    2.) Why I came up with the idea, the plan has resolution IV. Wikipedia says:
    "If N is a power of 2, however, the resulting design is identical to a fractional factorial design, so Plackett–Burman designs are mostly used when N is a multiple of 4 but not a power of 2 (i.e. N = 12, 20, 24, 28, 36 …)"

    So according to Wikipedia, it should be identical to a fractional factorial design then? And when I looked up fractional factorial designs with 4 factors and 8 runs I got a resolution of IV. This is what confuses me.
     
  4. Miner

    Miner Moderator Staff Member

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    It is a Plackett-Burman design, but the columns are out of sequence from the standard design. PB designs are considered resolution III because there is aliasing between factors and 2-way interactions. However, a true resolution III design, such as you would get from a highly fractionated factorial is 100% aliasing. In a PB design, the aliasing is not 100%, but is only partially aliased, so it really falls somewhere between resolution III and IV.
     

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