Designing Mixture Experiments
gail_massari
| Updated on
A variety of JMP mixture designs options support experimental situations where properties of a blend of components depend more on the relative proportions than on the absolute amounts being mixed. See how to create, analyze and interpret the results of several types of mixture designs.
See how to:
- Understand the definition of Design of Experiments (DOE) and how experiment design is useful
- Perform trade-space analysis using models fit to a mixture DOE for performance and cost metrics.
- Understand what makes mixture factors (components) and formulation DOE different from other DOE techniques
- Create two mixture experiments
- A simple 3-component design using JMP Custom DOE platform to make the design fit the problem, not force the problem to fit a design
- A 5-component mixture design with three constraints and response data
- Visualize the processes with Prediction Profiler in Fit the Model platform
- Use both Square root Transformation of response using JMP) and Generalized Regression using proper non-normal distribution (using JMP Pro) to prevent Prediction Profiler from showing physically impossible predictions
- Learn about additional mixture DOE examples
- Seven-component mixture DOE with 5 and 7 constraints aiming to improve quality control and manufacture less expensively
- Using constraints to define mixtures within a mixture
- Finding a 3-component blend that is nearly as good as a 7-component blend
- Ten-factor design with 6 mixture, 2 continuous, 1 categorical, and 1 block variable
- Incorporating additional constraints including holding some of mixture constant
- Space-Filling mixture DOE for computer chemistry simulation
- DOE for reverse engineering formulations
- Predicting chemical composition from fewer test blends by modeling spectra using JMP Functional Data Analysis
- Seven-component mixture DOE with 5 and 7 constraints aiming to improve quality control and manufacture less expensively
Questions answered by Tom Donnelly @tom_donnelly and Scott Allen @scott_allen at the 2024 live webinar:
Q: How do you decide the direction of the inequality sign when building linear constraints?
A: You need to think about it or write it out algebraically. From a point of view of the Ternary Plot, the blue triangle and the green triangle get defined by that inequality. And then that starts the algebra. See video below.
Q: How would you incorporate continuous factors, like curing or drying times, into mixtures.
A: That requires custom design. The example shows you all the steps. It has the 6 mixture components, but then it also has a cure time and an associated temperature. See the 10-factor example (JMP Complex multi-factor custom design.pdf).
Q: What is the difference between selecting None vs Specify for Define Factor Constraints?
A: None will mean that there are no specified constraints. If you would like to Define the Constraint you can select Specify to define the constraints.
Q: How did you zoom in on the Ternary Plots?
A: It is a few small steps. Remember if you rerun the Prediction Profiler after you zoom in, the Ternary Plot will refresh and you will lose the zoomed area, of course. See video below.
Q: If I don't want to specify linear constraints, would this affect my final analysis?
A: You don't have to have to have constraints to do a mixture design. We're just illustrating it, because more often than not, that knowledge of the chemistry comes into place is sort of very early on.
Q: If you're changing one mixture term and it affects the others and VIFs are unreasonably high, how do you get around the model being biased from that collinearity or multicollinearity.
A: I generally live with it. I think you'll find that the VIFs with mixtures can be all over the place. And there may be a lot of correlation. Particularly when you start getting into relatively trace components and mixtures, you have very thin regions. I am less worried about trying to interpret coefficients with a mixture than I am trying to interpret what are the predictions doing in this hyper triangular space.
Resources:
- Seven-component mixture DOE with 5 and 7 constraints using “mixtures within mixture”
- Ten-factor design with 6 mixture, 2 continuous, 1 categorical, and 1 block variable, including additional constraints including holding some of mixture constant
- Video Space-Filling Mixture DOE for Computer Chemistry Simulation, An Uncertainty Quantification Case Study Using Space-Filling Designs With Mixture Variables for Dete..., Melissa Jablonski, Douglas Ray, and Edward Cooke, JMP Discovery Summit 2017
- Video: Design of Experiments for Reverse Engineering Formulations, Predicting Chemical Composition from Fewer Test Blends by Modeling Spectra using Functional Data Analysis
- Candidate Set Designs: Tailoring DOE Constraints to the Problem, Christopher Gotwalt, JMP Discovery Summit 2021.
