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Custom design or mixture design? which one to choose?

Mathej01

Is there any difference between a mixture design and custom design with same factors treated as mixtures? Which would be better?

Accepted answers

Victor_G

Hi @Mathej01,

I will comment on some of your questions and responses:

"I dont really know how to explain the complexity . But i do have various types of responses , for example total price to rheological properties."
I perfectly see your point, price might be a very easy response to model (additive contribution of factors), whereas for rheological properties you may encounter some strong non-linearities depending on the ratio of some raw materials in the formulation. So a single apriori model sufficient and relevant for all responses may be difficult to find to take into consideration the differences in complexity between several responses.
"I am not really sure how different is space filling approach. I can only manage 20 experiment runs at most. Will that make any sense to do with space fillling approach?"
Here is a short overview and comparison between model-based and model-agnostic approach :

As you can see, the methodology behind these two designs types is very different, and may be complementary.
Concerning your budget for 20 runs, it depends on how many mixture factors do you have : the more factors you have, the more spread out will be the points in the experimental space, the higher will be your prediction variance (as the grid points/net will be more sparse, the prediction performances may be lower). Space-Filling approach are often used in combination with Machine Learning models (example (in french, soon in english) here from one of my use case : https://community.jmp.com/t5/Groupe-francophone-des/Compl%C3%A9mentarit%C3%A9-des-plans-d-exp%C3%A9riences-et-du-Machine-Learning/m-p/696018)

What may also be interesting could be to combine and use a model-based approach to place points in the edges/corners/vertices of your experimental space, and augment this design with Space-Filling points with the remaining experimental budget. This enable you to cover the full experimental space (borders included), and choose in the analysis phase a large variety of approaches, from different regression models to ML models.

I hope this complementary answer will help you,

All comments

Victor_G

Hi @Mathej01,

There is no "best" platform, it is highly dependent on what you plan to do.

You may have more design options directly available in the Mixture Designs platform and designs may be easier to apprehend and choose, as you already have a list of design types proposed with a short definition/explanation.
You can have a look at the list of the different designs available the Mixture Designs platform.
The Custom Design platform may be more relevant in case of specific constraints on the factors, like a several factors type involved (like mixture-process designs, a class of mixture experiments that incorporates non-mixture factors such as process, amount and type...), presence of hard-to-change factors, or the need for a highly customized model. Also the definition of constraints has more options in the Custom Design platform than in the Mixture Designs platform, and you can use a candidate set in the case of a very complex and constrained experimental space : Candidate Set Designs : Tailoring DOE Constraints to the Problem

The choice of the platform highly depends on a number of points, that may be answered through this list of questions (not exhaustive) :

What is your objective ? Predictive model, exploration, explanation, a mix of these ?
What are your factors and experimental constraints ?
What is the level of complexity/non-linearity of your responses ?
Depending on previous answers, would you opt for a model-based approach (Optimal, Simplex Centroïd, Simplex Lattice, Extreme Vertices, ABCD design, focussing more on the edges of the experimental space) or a model-agnostic approach (Space-Filling design, focussing more on the inner experimental space) ?
Depending on previous answer, which model would be most appropriate to use (or Space Filling designs) ?
...

I hope this answer will help you figure out what could be a good approach for your topic,

Mathej01

Thanks @Victor_G ,

I dont have all the answers to the questions you have mentioned. MAy be you could help me to answer those.

What is your objective ? Predictive model, exploration, explanation, a mix of these ? My objective is to have a predictive model, the exploration and explanation is not my priority.
What are your factors and experimental constraints ?All my factors are mixture factors and have linear constraints between those factors.
What is the level of complexity/non-linearity of your responses ? I dont really know how to explain the complexity . But i do have various types of responses , for example total price to rheological properties.
Depending on previous answers, would you opt for a model-based approach (Optimal, Simplex Centroïd, Simplex Lattice, Extreme Vertices, ABCD design, focussing more on the edges of the experimental space) or a model-agnostic approach (Space-Filling design, focussing more on the inner experimental space) ? when i checked, only optimal and space filling seems to be feasible for my design. But that is my nextr question. I am not really sure how different is space filling approach. I can only manage 20 experiment runs at most. Will that make any sense to do with space fillling approach?
Depending on previous answer, which model would be most appropriate to use (or Space Filling designs) ?

I hope my answers and questions are clear to you.

Victor_G

Hi @Mathej01,

I will comment on some of your questions and responses:

"I dont really know how to explain the complexity . But i do have various types of responses , for example total price to rheological properties."
I perfectly see your point, price might be a very easy response to model (additive contribution of factors), whereas for rheological properties you may encounter some strong non-linearities depending on the ratio of some raw materials in the formulation. So a single apriori model sufficient and relevant for all responses may be difficult to find to take into consideration the differences in complexity between several responses.
"I am not really sure how different is space filling approach. I can only manage 20 experiment runs at most. Will that make any sense to do with space fillling approach?"
Here is a short overview and comparison between model-based and model-agnostic approach :

As you can see, the methodology behind these two designs types is very different, and may be complementary.
Concerning your budget for 20 runs, it depends on how many mixture factors do you have : the more factors you have, the more spread out will be the points in the experimental space, the higher will be your prediction variance (as the grid points/net will be more sparse, the prediction performances may be lower). Space-Filling approach are often used in combination with Machine Learning models (example (in french, soon in english) here from one of my use case : https://community.jmp.com/t5/Groupe-francophone-des/Compl%C3%A9mentarit%C3%A9-des-plans-d-exp%C3%A9riences-et-du-Machine-Learning/m-p/696018)

I hope this complementary answer will help you,

Mathej01

Thank you so much @Victor_G

It was helpful. I wish the video was in French though.