Designing Mixture Experiments - Part 2
wendytseng
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Q: How do we consider sub-components of an ingredient (raw material) in a mixture design. for example an ingredient which is made of 2 sub components?
A: There might be a few ways to include this in a model. If you had mixture component A, that was made up of components a1 and a2; you could include a continuous factor describing the ratio of a1/a2.
Q: In the example, do you also need the proofing time main effect?
A: When you include a process factor/mixture factor interaction, the process factor main effect is removed from the model.
Q: Could you please comment on the analysis models used for space filling and Scheffé cubics? I was under the impression that standard linear models won't work and we must use gaussian or other models.
A: When you specify model terms (including 2-way interactions or Scheffe cubic) in your design, you can use standard linear least squares modeling methods. If you generate a space-filling design, you may need to use other models, like Gaussian or Neural Net, or some specialized modeling in Generalized Regression.
Q: Is there an easy way to see how increasing my run budget would improve statistical rigor or power of the model?
A: Power of mixture designs is difficult to estimate because of the correlated factors. Design space coverage is a way to visualize this. Whether or not the points in your design are spread throughout the design in the regions where you want to the information.
Q: Does JMP do pseudo-coding under the hood, or do you need to specify that somewhere?
A: JMP does it. From Column Info, you can specify the type of psuedo-coding. If you are analyzing an experiment that has not been done in JMP, you will need to make sure the column properties are set.
Q: How did you ask the software to pick the factors to give the tallest bread?
A: Under the Prediction Profiler red triangle, I Set Desirabilities, and then from the red triangle Maximize Desirability.
Q: Why do you keep interactions in the effects summary with p value of 0.7?
A: We are just working with the model as provided without reducing it. You could certainly move terms in and out to see how that effects your analysis.
Because the model terms are highly correlated, though, you might choose to keep those model terms that do not appear significant and validate with confirmation experiments.
Q: How do you visualize mixture design spaces with more than three components?
A: These are commonly visualized with ternary plots with two of the three vertices representing individual components and the third vertices representing the sum of all other components. Here is an example of the Lubricant Formulation experiment that is in Strategies for Formulations Development, A Step-by-Step Guide Using JMP (Snee and Hoerl, 2016). Look at the first ternary plot at the top, Others = % Acid B + % Acid C.
Here is a short video that explains how to visualize design spaces for mixtures with more than three components.
Resources
- Mastering JMP Designing Mixture Experiments - Part 1 video and materials
- Design of Experiments for Mixtures Using Machine Learning Course by Predictum, a JMP Partner
- Design and Analysis of Mixture Experiments Course by Adsurgo, a JMP Partner
- Accelerating Innovation with Space Filling Mixture Designs, Neural Networks and SVEM (2021 JMP Discovery Presentation)
- JMP Pro 17 Remedies for Practical Struggles with Mixture Experiments (2022 JMP Discovery Presentation)
- Strategies for Formulations Development, A Step by Step Guide in JMP by Snee and Hoerl, 2016
