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DOE in mixture design with mixture in mixture approach

Greetings to all

Wishing this reaches all well, thanking all for the help and suggestions

I had been involves in a research project relating to develop a mixture and was introduced to DOE in JMP and did a basic learning on the software but I am finding it hard to develop doe for the purpose of experimental test. the details of the application in my case is follows. 

the property responses that I want to study seven(7) different property responses related to the proportions of the mixture constituents and find the optimal composition.

The material mixture that is being studied has four main components such as:

1. Adhesive components (A)

2. Filler components (B)

3. Activator component (C)

4. Reinforcing elements (D)

the component promotion can be explained with an example range the Adhesive components (A) is considered as the base of the mixture which is taken to be 10 units, the other components are selected base on the the filler and activator component as added in the ratio ranging from (1.5-2.5 times (A)) and (1.5 -2.7 times(A)) respectively. which yeilds to B =15-25 units and C= 15-27 units in the mixture the reinforcing component is considered in the range of 0-7% of (A) which calculate to a range of 0-7 units. The components A,B,C,D have individual components which is to be formulated as a individual mixtures. i.e the adhesive elements have four (A1,A2,A3,A4) individual elements that is to be mixed in A proportion such as (A1 = 70 -100%, A2 = 0-15%, A3 = 0-7.5%, A4 = 0-7.5%). the total A1+A2+A3+A4 becomes 10 units. the components of the element group B,C and D needs to be adjusted in proportions such that the quantity of the final mix should be satisfied.

such that  B1+B2+B3 = (1.5 TO 2.5) times of A

where B1 = 80-100% B2 = 10 - 20% and B3 = 0-10% 

similarly the quantity of the other components must be selected 

  The study needs to understand the optimal mix proportions of each elements and the effect of the individual elements on the considered properties of the mixture. the performance of the mixture is evaluated in terms of 7 performance responses measured through the experiments.

 

1 REPLY 1

Re: DOE in mixture design with mixture in mixture approach

The generally advised approach to mixture-within-mixture designs is to combine all of the mixtures into one mixture, and to express the factors levels as percentages of the whole mixture. For example, if your mixture A can be between 10% and 20% of the whole mixture, and mixture factor A1 can be between 15% and 30% of the A mixture, then the values for Factor A1 in the custom designer would be .015 for the low end (15% of 10%) and .06 for the high end (30% of 20%). You would repeat this for each of the factors, then run the DOE.

That being said, this sounds like a very large experiment. If I assume C and D each have only 3 mixture components, then you'd have 13 mixture components, which would generate a DOE with a very large number of runs (180+ for just interactions, 500+ for interactions and curvature). While the design itself would be correct, the likelihood of controlling all external factors tends to be diminished with large experiments, meaning you might not be successful, even though you designed the data portion of the experiment correctly.

Is it acceptable to consider screening experiments up front to reduce the total number of factors being studied?