Determining Alph

Nimaxim — Tue, 16 Jul 2024 20:15:33 GMT

In RSM and CCD design, To prevent negative values in runs, is that possible to enter factor ranges in terms of alpha instead of using upper and lower factor values?

Re: Determining Alph

Victor_G — Wed, 17 Jul 2024 07:09:53 GMT

Hi @Nimaxim,

I'm not sure what you imply regarding the use of alpha instead of using upper and lower factor values ?

Just to clarify, there are two classical Response Surface Model designs available :

Central Composite Design is often used as the last step of augmenting a factorial design : The study involves generally the screening of different main effects (to know which factors may enable a better resolution for example), and once identified, the design is augmented to include 2 factors interactions and quadratic effects, resulting in a CCD, in order to fully optimize the process and find the best analytical settings. If your optimum area is expected to be in the centre of your experimental space, CCD might be a good design option.
Box-Benhken design is used in litterature as one of the design having the best "precision", as more power is available for quadratic power, and this design has uniform precision in the experimental space, often for a lower number of runs than for the CCD. More infos on Box-Benhken : The Open Educator - 4. Box-Behnken Response Surface Methodology
If you expect your optimum to be at the edges of your experimental space, BB might be a good design option. Also note that you won't have factor values below -1 or above +1 with this design, so if you have set physically feasible values -1 and +1 for your factors, a Box Behnken design can always be run, since you don't have points in the corners of your experimental space (unlike CCD).

Concerning Central Composite Design, there are three main types of designs depending on the alpha value :

Circumscribed (>1),
Face-centered (=1)
Inscribed (<1)

More infos about the several CCD (circumscribed, face-centered, inscribed) :

5.3.3.6.1. Central Composite Designs (CCD) (nist.gov)

5.3.3.6.3. Comparisons of response surface designs (nist.gov)

See the screenshot with the several options in JMP (DoE, Classical, Response Surface platform) with coded factors values with -1 and +1:

Only the "Inscribe" checkbox option or "On Face" design option will create star points with values equal or less extreme than the boundary values of your factors (-1/+1).

If you want to prevent negative values in runs, you should avoid circumscribed CCD, and aim for face-centered or inscribed CCD types. On a similar topic, I showed that the farthest the star points are from the centre of the experimental space :

The higher the power for main effects and quadratic effects, but the lower the power for the intercept,
The higher the variance in the centre of the experimental space, but the lower the variances at the border of the experimental space.

The choice of the value for the star point is a compromise between physical feasability of the runs (can you extend the factors range below the -1 or above +1 coded values) and the objective(s) behind your CCD.

Maybe this webinar can help you set up your RSM design (CCD with Classical Response Surface platform or with Custom design platform) :

Hope this answer will help you,

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Determining Alph

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