Mixture design DOE analysis

[#1]

hi,

I have a mixture design with 3 factors and 6 runs initially to perform my experiments, before performing experiments I would like to know whether my design is valid or not? I have used I optimal criterion and have 6 runs without centre points, with 3 mixture factors in 2 levels

[#2]

Hi @Statexplorer,

It might be very difficult to answer you since there is not enough information or context provided.

However, based on the limited informations, I may have some questions and discussion.

Recreating a design in the same conditions as yours, it seems you have assumed only a main effects model :

• What is your objective with this design and what is your experimental budget/constraint ?
• What is your system complexity ? Why are you assuming such simple model for a mixture design with few factors (3) ? You won't be able to evaluate mixture of factors with this setup (each experiment only involves 1 factor), so you can really miss a good combination of components as you're not investigating mixtures.
• I'm also a bit surprised by the use of I-optimality since you assume a model with main effects only. The optimality criterion here won't change anything, you will end up with same/similar designs no matter the optimality criterion with the settings you have.

I would recommend to try other mixture designs models, depending on the complexity assumed and your experimental budget :

• Using Custom design and specifying 2-factors interactions, you'll end up with mixtures including up to 2 components for a default recommend runs number of 12 (and minimum at 6 runs) :
  
• If you have no constraints on the ranges of your mixture factors, I would also recommend trying and comparing classical Mixture designs : Examples of Mixture Design Types
  • Typically, the Simplex Centroïd design is an interesting choice, providing for a minimum of 7 runs (you can add replicate runs) three experiments with 1 component, three mixtures of 2 components, and one centre point with 3 components : 
    
  • An other interesting option is the use of Augmented Simplex Centroïd (available through the "ABCD design" option), which provide the same points as the Simplex Centroïd design and adds 3 points corresponding to mixtures with 3 components. You can use these 3 added points as validation points of the Simplex Centroïd design and associated model (main effects and 2-factors interactions), and/or use them to estimate more precisely model's parameters :
    
  • Finally, you could also try Space-Filling mixture designs or Simplex Lattice designs if you want to explore homogeneously your experimental space without assuming a specific model. However, to be efficient, these designs often require a larger number of runs than model-based designs : for Space-Fillings, JMP recommends 10 runs per factor (but you can adjust the total number of runs as you want), and for Simplex Lattice designs for 3 mixture factors, JMP recommends 21 runs. The larger number of runs and good experimental space coverage help using flexible models, like Machine Learning models.

I hope these few points will help you,

[#3]

Hi Victor Thanks for your reply,

The objective is to screen some different batch of materials came from different vendors, we can take the material qty in percentage, which adding up should be 100.

No budget constraints as it would be first DoE from my side, I wanted to start with fewer experiments I have considered all Two-way interactions with 2 replicates and no centre points with I optimal criteria.

All 2FI i have given as If possible, it can include in model

I have considered I optimal as It was told to me that I was suitable optimal criteria for mixture designs.

As this the First DOE I have considered very less experiments to check any error occurs

[#4]

Hi again,

Since you mention a screening of different batches from suppliers, I wonder if you are really in a situation of Mixture designs only ? It sounds like you could use factorial designs (if there is only one raw material batch at a time), or custom designs (to enable mixtures in presence of various batches).

I don't understand what are your factors in the design and the link between the raw materials and the batches. Can you also share an anonymized design table to better understand your design settings ?

Could you provide more information ? :

• Do you have 3 raw materials in formulation (adding up to 100%), with each of this RM having several batch options ?
• Are the ratio/relative quantities similar or do you have strong differences between them (like A+B represent 98-99% of the formulation, and C represents the remaining part ?) ?
• How many batches do you have to screen ? How do you select them ? How representative is this small batches subset compared to the population of batches you may receive from the suppliers ?

Hope my questions make sense with your topic,