How should I modify my DOE when I can't match the prescribed levels of a continuous factor?I am looking to design a set of experiments to fit a response surface model with 2 categorical factors (2 levels each) and 1 continuous factor. Entering the categorical factors is not a problem, but when I add the third factor as continuous, I noticed that the design only selected the low (0), high (1), and midpoint (.5) for that factor.
Unfortunately, I do not have materials available to compound the midpoint value. I have materials ready to go for the low and high levels, as well materials equivalent to the 0.3 and 0.7 levels. I still want to fit the full response surface model, so could I replace the 0.5 level with either the 0.3 or 0.7 levels? Is there a better way to incorporate all 4 materials that I have on hand into the design?
Any guidance is greatly appreciated!
Re: How should I modify my DOE when I can't match the prescribed levels of a continuous factor?Another possible option is to make the factors Discrete Numeric with 4 levels. JMP will force each of the levels into the design, treat the factor as continuous, but only allow the specific levels that you specify. In order to do this, JMP will add higher order terms to the model, but will make them "If Possible". Leave those terms in, changing any of them to "Necessary", if appropriate.
Re: How should I modify my DOE when I can't match the prescribed levels of a continuous factor?First off, I noticed your continuous variable ranges from 0 to 1 and not from -1 to 1. That is not a problem, just unusual and I will take it from here as is.
My solution to this case is to use disallowed combinations. Say you specify your continuous variable as X1. After you set your factors in the Custom Design window, go to the tab "Define Factor Constraints" and select "Use Disallowed Combinations Script". As you select this option, the window "Disallowed Combinations Expression" opens up. Inside this window you type the following constraint (copy and paste what is inside the " " marks but not the " " marks): "X1 >= 0.3001 & X1 <= 0.6999". These two constraints define the range of X1 that you do not want in your DOE table.
You may find it funny that 0.3001 and 0.6999 are used instead of 0.3 and 0.7, respectively. The reason for that is that if you use 0.3 and 0.7 instead, you may "push" the algorithm that searches for the best design to consider X1 levels lower than 0.3, and higher than 0.7 instead of exactly 0.3 and exactly 0.7, respectively - and you don't want those. So you trick the algorithm by using constraint levels very close to those you want like 0.3001 and 0.6999. Try using 0.3 and 0.7 instead and see for yourself what you get for further clarification.
You may be also curious to know how much you lose because of this constraint. To that purpose you will find attached two JMP table files. One with the resulting DOE with disallowed combinations that respects your constraint, and another without any constraint. Both use n = 14 which is the default number of runs for the response surface model with 1 continuous and 2 categorical variables with 2 levels each. If you compare both designs - open both tables and in one of them go DOE>Design Diagnostics>Compare Designs, select both tables and hit OK - you will see that there is relatively little lost in terms of prediction variance. In the comparison report you get you will see the plot below that shows Prediction Variance vs. Fraction of the Space. Even though the area under the curve is higher for the constrained range design (blue), it is not higher by much in relative terms. So, you might have thought that you would lose predictive power by constraining the X1 range, and you do, but not much.
