I think that Taguchi its very useful, however, as I do not have much experience using these techniques because my experiments are expensive very time consuming.
many thanks for the response Fausto, the interactions are : FG,FA,FB,GB. My experimental experience with this type of process shows thas this interactions are really important but its necessary prove it with statistical basis .
There is something else you could try, Optimal Designs. Are your factors categorical or continuous? That can help determine what type of designs you can use.
@Fausto Galetto
Many thanks for the design that you made for my case, I will try to put it into practice
@Andrew Ekstrom
Many thanks for your response. My Factors are Continous. I would like to know and learn about optimal designs, Can you give me some information and hints for try to use this type of optimal designs?
One of the best books I've read on the subject is "Optimal Design of Experiments: A Case Study Approach" by Peter Goos and Brad Jones.
A, D or I optimal? Are there any contrasts that we should not test? Do we want to look at quadratic terms? What is the number of runs we have to work with? Since factors are continuous, we can test all the factors at 3+ levels. Would that be of interest?
With 36 runs, I can create a model that will find ALL 2-way interactions and quadratic terms for for your last 2 factors. With 19 runs, I can find all main and quadratic effects, plus the 4 interactions, plus have 5 extra runs to create an error term and look for model validity, or look for other interactions, or create blocks in the design.
What are the goals and constraints for the design?
Optimal designs are called that because they fulfill the criteria for Optimal Regression, as proposed about 150 years ago. They are not orthogonal, because they don't need to be. Have you ever seen an observational study where the input variables were orthogonal? No, because nature doesn't care about orthogonality.
Mixture designs are not orthogonal either.
What is nice about optimal designs is that you can customize the design to your needs. You change the design to conform to you experiment's design space, not force your design space to conform to your experimental design. The optimal designs lose some orthogonality in order to do this. The VIF of the terms in the designs is below any rational criteria for that. Even in designs where the VIF for a term is particularly high, like an A3BC2, optimal designs can let you see them.
Another nice thing about optimal designs is that you can run a smaller block, see how that turns out and add an additional block of runs of any size and add that to your original design.
Suppose that some of Oscar's factors are expensive or time consuming. Doing a 36-run design might not be feasible or practical. The 19 run optimal design fulfills his needs for the initial design. He can come back later and add another 4-5 runs to see if his initial results were both accurate and if there happens to be an issues with blocking. He can also use those runs to find if there are other interactions he needs to be aware of.
If there is an issue where he need can't change a factor easily, thus requiring a split plot design, he can go back and modify the design as needed. If certain combinations of factors are dangerous, he can go back and modify his design.
In a resource constrained world, optimal designs are optimally suited for this reality. Would it be nice if everyone everywhere could use a block from a larger orthogonal array to do their experimentation? Yes, it would. Is that a reality most of us live in? No.
Why should we use your data? Why not real data? In the 19 run design, you have 5 extra data points beyond the minimum. If you can't figure out how to analyze any 2-way interaction with the designs, you need help.
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