Hi @gam1,

Welcome in the Community !

Before diving more in-depth into your design, some few comments and questions:

- Why are your factors "Discrete Numeric" with 2 levels if you want to have a surface response model ? To assess curvature of the response related to one or several factors, a third level is necessary. Else you'll only use the min and max levels of your factors, so only including some possible curvature through interaction effects.
- Are your factors really independent ? The constraint formula involving them looks like 2 ratios, so this is why I'm asking the (perhaps naive) question.
- It seems in your explanation you have inverted D and B ("But excluding all combination of factors that give a value of (A2/A1)*(B1/B2) lower than 0.1 and higher than 10."), but with the screenshot it all makes sense, it's only about factors A1, A2, D1 and D2.
- Finally in your factor windows, take care that the min values for each factor is on the left, the max on the right (it is reversed for D1 and D2).

Concerning your constraint, since it is Disallowed combinations, it looks ok (with the inequality being not strict based on your needs, as emphasized by @statman).

I am not sure why the custom design still proposes some runs that are not adequate regarding the constraints.

My workaround would be to use a candidate set through these steps:

- Create your candidate set, a datatable for A1, D1, A2, D2 and formula uniform distributions (with the limits you have set if factors can be considered as numerical continuous, probably for D1 and D2) or random integer (from min to max) if you consider these factors as discrete numerical / integers (probably for A1 and A2). I did this for 1000 rows.
- Using a data filter on this datatable, exclude points that do not respect your constraint.
- Use the Custom design platform on your candidate set datatable, use "Select Covariate Factors" and select your 4 factors.
- Specify your model and the number of runs in your design (17 should work). You can check "Allow covariate rows to be repeated" if the runs can be replicated in your experimental setup.
- You obtain a design that do respect your constraint :

Attached you'll find the datatable used for the candidate set approach, with script containing the data filter and one possible RSM optimal design.

If you can provide more infos about the type/nature of the factors (continuous ? discrete ? how many levels if discrete ?), that would greatly help find a suitable solution working for you (as I'm not sure my assumptions on your factors are true).

In the meantime, you can have a look at these ressources :

Demystifying Factor Constraints : JMP Blog post by @Jed_Campbell on how to include factor constraints in a DoE

Candidate Set Designs: Tailoring DOE Constraints to the Problem (2021-EU-30MP-784) : Presentation by Chris Gotwalt showing how to use candidate set to build DoE in case of complex constraints.

Hope this may help you,

Victor GUILLER

Scientific Expertise Engineer

L'Oréal - Data & Analytics