Hi @DRC92,
Welcome in the Community !
The choice and analysis of DoE really depend on your prior knowledge about the system, and the number of factors, constraints, randomization restrictions, noise/signal ratio, ...
You mentioned that you may have as little as 2-3 factors and as high as 8-9 factors. Do you already know the influences and importances of all the possible factors in your system ?
If not, I would recommend starting with a Screening design, to detect important effects and factors in your system.
Once these important effects identified, you can then augment your design to add some points to refine your model (and increase predictivity) and optimize your response(s).
Your initial screening design should include as much factors as possible with large factors range, to identify which factor(s) are important and active in your system.
- Definitive Screening Design may be an interesting choice in the absence of factors constraints (and for 5+ continuous factors, and limited number of 2-levels categorical factors), as it is a powerful 3-levels screening design which can detect main effects, interactions and quadratic effects, for a very limited experimental budget. Having 3-levels for continuous factors help avoid "binary" responses with very high or very low values, or using only "absence/presence" settings for the high and low levels of the factors.
- Custom design (D/A-Optimal screening designs) may also be an interesting alternative, enabling to include various factors types, constraints, and randomization restrictions (for example if you need to setup your plate experiments with a defined number of experiments by row and columns), with full flexibility on the assumed model and what you want to detect.
I hope this first answer will help you,
Victor GUILLER
L'Oréal Data & Analytics
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)