Hello!
I went through the 2 level factorial design to screen factors, and now I am moving to the characterization using CCD.
The coded alpha value in Design Expert v.13 is set to ca.-1.4. However, one of my factors assumes discrete values. I can change the alpha value to e.g. -1.5 (I go with even numbers so it works fine). My question is, how does such a change affect the design? Will I encounter any issues?
Value of alpha plays a role in determining the rotatable nature of the Central Composite design.
for spherical designs, the design points must be located at same radius (square root of 2 = 1.414..., in case of your design) from the origin, that is, the center point of the design.
If you want to set alpha = 1.5, make sure all new design points are still at same new value of radius ( alpha=1.5), in your design.
I recommend the following books in this regard:
Chemometrics, by Ed Morgan
Response Surface Methodology book by Myers, Montogomery and Cook.
You will not encounter issues. It serves the practical purpose that your model error is slightly reduced at the Design Space's rear ("faces"). (Anybody correct me if I am wrong).
However, you perform CCD normally to get an optimum set point and that should be never at the Design Space's rear but somewhat in the middle of your Design Space: So if you see that your optimum set point is close to the rears then you probably need to augment your design anyway to get more confidence.
If you do not have resources to add augmentation / confirmation runs, I'd go for the recommended alphas - but +/- 1.5 or 1.414 is quite similar anyway. Often people tend to use alpha of 1 ("CCF") and then you can start discussing, but your deviation is really small.
Aris Perrou Thank you for the answer.
Do you think running a 3 level factorial design instead of CCD with determined discrete values might be another solution to this issue?
It might have more runs, no?
There is a 80 minute presentation by Statease, describing how to sophisticatetly assess if "more runs", etc, are really necessary. It explains the concept of "Fraction of the Design Space", FDS, graphs.
https://www.youtube.com/watch?v=6CUa_n6ZEj4
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