Central Composite Design or Custom Design (w/ Discrete Numeric)?

[#1]

Hello,

I have just finished doing a screening design and the 3 resulting main factors of interest are: temperature, time, and the dielectric constant of the solvents.

I would like to do an RSM with these 3 factors. However, the dielectric constant values are discrete (0.1, 6, and 37) which I cannot replicate in the central composite design menu. When I go with the custom design and set the discrete numeric factor it omits the "middle" point (i.e., the level at 6).

I was wondering how I could get the custom design to include it?

Thank you!

[#2]

Just to clarify, the left side of the image is the custom design in which the dielectric constant value of 6 does not appear, while the right is the standard central composite design.

[#3]

Why not just use solvent just a categorical factor?

Below I have posted a script for generating the custom design with the discrete numeric.

[#4]

DOE(
    Custom Design, 
    {Add Response( Maximize, "Y", ., ., . ), 
    Add Factor( Continuous, 1, 3, "Time", 0 ), 
    Add Factor( Continuous, 130, 170, "Temp", 0 ), 
    Add Factor( Discrete Numeric, {0.1, 6, 37}, "Dielectric Constant", 0 ), 
    Set Random Seed( 1193 ), Number of Starts( 78402 ), Add Term( {1, 0} ), 
    Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), 
    Add Potential Term( {3, 2} ), Add Term( {1, 2} ),
    Add Term( {1, 1}, {2, 1} ), 
    Add Term( {2, 2} ), Add Term( {1, 1}, {3, 1} ),
    Add Term( {2, 1}, {3, 1} ), 
    Set Sample Size( 15 ), Optimality Criterion( 2 ), Simulate Responses( 0 ), 
    Save X Matrix( 0 ), Make Design}
)

[#5]

Hello louv,

I am interested in modulating the dielectric constant (the solvent itself is less important), so it makes more sense to me to set it as a continuous factor!

Thank you for you reply and the script, I appreciate it!

Best regards,

Tehol

[#6]

If that is the case should you consider the solvents as mixture factor?

[#7 · Accepted solution]

Hi @Tehol,

Trying to reproduce the Custom Design, I don't have the same problem you mentioned (see capture). Did you specify that the discrete numeric had three levels ? And clicked on RSM to have all main effect, interactions and quadratic effects in the design/model ?
I attach the file I used to generate the Custom Design if you want to use it (or you can use the script done by @louv).

Also something to consider : why not augmenting your original screening design with the three factors of interest by adding terms in the original model ? By augmenting your previous design, you'll keep valuable informations from your original experiments, and you may need a lower number of experiments to do, compared to starting from zero.

For the CCD, by default the middle point (coded 0) will be at the middle of the range (you get 18.55) but you can manually change it on the table if needed (even if you lose some optimality and "space covering" in your design by doing so).
Also perhaps more tricky, but doing a transformation log(X+1) on the dielectric constant of the solvent will bring you to a linear scale where the three levels are more equidistant from each other, but it may be more complicated to interpret the results with this transformation, since you'll have to revert the transformation to know the real dielectric constant value.

I hope this first answer will help you,

[#8]

Hello Victor_G,

That's odd, I wasn't able to get the same capture as yours -- I will attempt it again following your instructions.

I don't think I'm comfortable enough with DoEs and analysis in general to attempt augmenting my original design.

The experiments aren't expensive to run in any case, so I think I'd rather begin with a clean slate --- it also allows me to practice more!

And I did not think of transforming it into a log-scale, that's brilliant! I think I may pursue that avenue.

Thank you,

Tehol

[#9]

Did you remove the quadratic term from the model (Estimability = If Possible) before clicking Make Design?