Hi @wzm,
Just to be sure to have understood your objective : you want to select one amino-acid and one vitamin among a set of these raw materials to have the best combination between the two and obtain the best results ?
If yes, as you seem to mention "screening" in your question and post (or at least the automatic translation tool has translated your original question as : "If the experimental independent variable is categorical and the response is continuous, can an orthogonal design be used for screening?") and considering the relatively large amount of different raw materials you want to study, I would not try to find the best combination between amino acids and vitamins in a first design (or only in one design), as it can represent a large number of experiments to do to test all combinations (160 unique combinations).
One option could be to subset a number of different amino-acids and vitamins in order to study the variation of your continuous response with limited number of levels for each factors. Instead of testing all 20 different amino-acids and all 8 vitamins, you could select 5 amino-acids and 4 vitamins (for example), so that these molecules express the maximum variability in terms of molecular properties/descriptors. There are multiple ways to select the raw materials, but using the chemical structures, molecular/chemical properties, molecular descriptors values can help in comparing the raw materials and select only those with the highest chemical variability.
I described this option in a previous discussion and this method is also explained in a presentation : Efficient DOE of one multi-level (3+) categorical variable and many continuous variables
Increase Efficiency and Model Applicability Domain When Testing Options That Are at First Glance Mul...
You can then analyze the results of the continuous response thanks to the continuous molecular descriptors/values that you can use as covariates. Using continuous factors instead of categorical factors represents a great gain of information :
https://community.jmp.com/t5/Abstracts/Coding-with-Continuous-and-Mixture-Variables-to-Explore-More-...
The big advantage of this approach is that you avoid a single DoE "brute-force" approach involving a lot of experiments, and you can build your knowledge and start optimising by iteration : once you understand which properties of your different molecules have an impact on your response, you can then select other raw materials (amino-acids & vitamins) and refine your model to have more in-depth understanding about interactions and specific order effects, and optimize the response.
Hope this discussion starter and perspective may help you,
Victor GUILLER
L'Oréal Data & Analytics
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)
