Hi @loganshawn,
From your description, there may be (at least) two options to consider :
- Either you work with the individual components/raw materials: you find the components of each mixture and do a mixture design with the individual components, and define appropriate range for each factor based on your domain expertise and experience with the mixtures, and build a mixture design. Depending on the number of individual components, this option may require a high number of experiments.
- Or you work with the mixture preparations : you can then build your mixture design based on your 4 mixtures, and define appropriate ranges for each based on your experience. Once you find the optimum mixture (ratio) of the 4 mixtures, you can calculate the optimal amount for each constituants if you have the composition information for every mixture preparations.
There are indeed a lot of options for mixture design, from classical ones (Scheffe Cubic for example), to more specific ones (Custom designs and Mixture Space Filling). You can see an overview of available mixture designs here : Overview of Mixture Designs (jmp.com) and here : Examples of Mixture Design Types (jmp.com)
The choice will depend on several criteria, such as : experimental budget, expected prediction precision/variance in your experimental space, "continuous" or "discontinuous" response surface, model-based vs. model-agnostic approach ...
Some differences between models and terms used in different models :
- In Scheffé cubic model (done in Custom Design), you'll be able to create a model with main effects, 2 mixture factors interactions and 3 mixture factors interaction, for a total of 30 runs recommended by JMP (see screenshot). You can add manually the 4 factors interaction for not extra cost (JMP doesn't seem to add runs in the "recommended runs number" when you add this term in the model, but it does change the minimal amount of runs needed from 20 to 21 because of this extra term added).
- In Simplex Centroïd design (done in Classical -> Mixture Design), you are doing mixtures with up to 4 components for a total of 15 experiments recommended by JMP (see screenshot). You have fewer runs than the previous design, but at the expense of a larger relative variance prediction in your experimental space.
- A Space filling Mixture design might also be considered, in this case for 4 factors JMP recommends 40 runs. The advantage of this design is the homogeneous repartition of points/runs in your experimental space, without pre-defined model (it's a model-agnostic approach). That means you should be able to use other modeling approach for analysis, like Gaussian Process, or techniques from Machine Learning such as Support Vector Machines, Tree-based methods, Neural Networks, etc... The validation of such models could be then done with train/validation/test sets or SVEM method (Using Design of Experiments Methods for Efficient Modeling & Simulation - JMP User Community). But it comes at the expense of more aliasing (correlations) between factors, so it might be more difficult to understand which mixture factors or interactions is driving the response(s) (see screenshot Matrix_correlations_designs).
So the choice is up to you, if you prefer a "causal" model (Classical Mixture designs and Custom designs with pre-defined model) or only a model with good predictive performance but with limited knowledge. Based on the previous post you made, a Space-filling approach was considered for one of your similar topics, but you may change your mind depending on your objective and experimental budget.
There are so many things we can tell about Mixture designs, you can check on the community similar topics and the webinars dedicated to this topic (Designing Mixture Experiments - Part 1 - JMP User Community, Designing Mixture Experiments - Part 2 - JMP User Community, Accelerating Innovation with Space Filling Mixture Designs, Neural Networks and ... - JMP User Commu...).
I hope this first (long) answer will help you in your reflexion,
Victor GUILLER
L'Oréal Data & Analytics
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)