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DOE Mixture Design with imbalanced disallowed combinations

nliu6

Hello,

I read the post regarding DOE mixtures with disallowed combinations of components.

I have a similar problem here. I have three candidates for one mixture component (A1, A2, and A3). Only A1&A2 or A3 is allowed. The ratio of A1 and A2 is not set.

Is it possible to make one design for all runs? Otherwise, I will separate them into two mixture designs.

Accepted answers

statman

My continuing thoughts:

There is no perfect design or approach. Some will be more effective, some will be more efficient and each may differ in the resources required to complete. I would design several options, predict all possible outcomes from each experiment design and weigh the pros and cons of each.
When I think of optimization, I recommend to have all continuous variables.
Seems to me you need to decide which way to handle A and B before including them in the mixture design with the other 2 components?
I'm confused by your using categorical for A & B and also having A1/A2 ratio as continuous. What would the levels of A be? Would the levels of A conflict with the A1/A2 ratio? What you might consider is using 2 different ratios for A1/A2 as levels for factor A.
Not sure what B is other than you indicated there were 3 of them possible? What are the 3 different B's? Same questions as for A are any of them cheaper or easier to process?

All comments

statman

Just to clarify, you can use a mixture of components A1 & A2 or just component A3? If this is the case, it seems like you should decide whether to use A3 or A1/A2 first. Questions:

1. Is there more than one response variable of interest?

2. Is there a cost advantage to the A1/A2 m mixture vs. A3?

3. Do you understand the variability of the incoming components A1, A2, A3? Do some vary more than others?

4. What is the "mixing process? Which variables would be easier to process?

If it is just A3, it does not look to be a mixture design as it is one factor.

nliu6

There are 6 components in this mixture and 2 are constant. There are 10 responses. We have two options for component A: a mixture of A1/A2 or only A3. All three candidates are quite consistent from batch to batch. The A1/A2 mixture offers slight cost advantage. We also have three candidates for another component B: B1, B2, and B3. I am thinking to add a categorical variable for B on top of the mixture variable. But not sure if I can capture everything in one design.

statman

My thoughts:

1. The 4 variable components are A, B and 2 others (plus the 2 that are "constant")? Or are you saying A1/A2 or A3, B1, B2, B3?

2. Since you are considering an optimization experiment (mixture designs are for optimization) are you ready to do this? What I suggest is that you first understand processing variables (e.g., mix speed, mix time, temperature, etc.) and NOISE before moving to optimization (You may have already done this). If those other variables aren't understood, then you find a response surface that is only useful under those specific conditions...when those conditions change, so may the surface.

3. If you have other variables to consider, you can try ratios of the mixture components to include with other variables. While this may not provide optimum conditions, as long as you go bold on the ratios, you can compare the significance of those effects to the effects of processing variables and noise.

4. If you are confident you have a consistent, predictable process, then by all means move into optimization. Since you have 4 components. JMP will be quite helpful in setting up and helping to analyze the design. The emphasis on the analysis is on the contour plots rather than statistical significance.

nliu6

1. The 4 variable components are A, B and 2 others (plus the 2 that are "constant").

2. We explored the process variables and have them set now.

4. I am thinking of a design with 4 mixture variable, 2 categorical variables for selection of A and B, and 1 continuous variable for ratio of A1/A2. Not sure if this is the best approach. Or it is better to split it into two designs with the two options of component A.