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Nov 1, 2013

A 4-factor definitive screening design as a response surface design alternative

cars beforeI’ve been a huge fan of definitive screening designs from the moment I first read about them. I’ve also been excited by Bradley Jones' new approach for analyzing definitive screening designs.

As my second experiment with dyeing toy cars had promising results, it seemed like the right time to better explore the factors I had narrowed down – and a definitive screening design is a great way to do it.

For the purposes of rating the dyeing, I decided to stick with one color this time. With multiple colors, it was sometimes difficult to determine when one color was better than the other. I was ambitious with this experiment – the color used for dyeing was red, which was the problematic color in the first experiment. I knew that I wanted to use additional heat in this experiment based on the previous results, so the factors I was interested in were as follows:

  • Amount of vinegar: 0%-50%
  • Dye amount: 1 tsp – 2 tsp per cup of liquid
  • Time in liquid: 10 minutes – 30 minutes
  • Heat setting: 1 – 3, based on the ticks on the knob for the burner on the stove
  • There’s certainly the possibility of active quadratic terms and interactions in this design space.

    Why use a definitive screening design?

    • The 13-run default definitive screening design for four factors is based on six factors – those two unused “fake” factors can give an estimate of the pure error assuming third-order and higher interactions are negligible.
    • The smallest design from the response surface design platform is 27 runs, doubling the amount of resources I need.
    • Fitting the full RSM model in Custom Design will require 15 runs, and the model terms will have some non-zero correlations among them, which will affect model selection. I still want to find the most important effects and not fit the full RSM model, so my preference is to use the orthogonality of effects that comes from the definitive screening design.
    • What orthogonality of effects?

      If you’re still new to definitive screening designs, I highly recommend that you start with Bradley Jones' first blog entry and original paper, but to summarize what I get from the 13-run definitive screening design:

      • Main effects are orthogonal to each other.
      • Main effects are orthogonal to two-factor interactions and quadratic effects.
      • The model including all main effects and quadratic effects is estimable.
      • None of the second order effects are fully confounded.
      • For the 13-run design, I can fit the full RSM model for any three factors.
      • And now to create the design...

        Once I had decided on using a definitive screening design, creating the design was simple. I went to DOE->Definitive Screening Design and entered my factors.

        One last thing: I had two different cars to use that should be treated as blocks. Fortunately, the definitive screening design platform allows for the addition of blocks that are orthogonal to the main effects.

        My final design setup looked like this:


        Next time

        I'll share my results with you in the next blog post, but I will say that it is possible to get the red to stick.

        Thanks for reading!