Designing Mixture Experiments

gail_massari — Thu, 24 Oct 2024 17:24:40 GMT

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.

(view in My Videos)

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

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.

(view in My Videos)

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.

(view in My Videos)

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 Deterministic Data, 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.

Re: Designing Mixture Experiments

Paul_J — Fri, 25 Oct 2024 12:45:42 GMT

Great presentation ... Thanks! ... A couple of thoughts come to mind ...

First, relating to "why DOE", I like to say that DOE tells you what happens when you turn more than one dial at the same time.

About the question on VIF's ... The coefficients in mixture models do not represent factor effects as they do in traditional DOE. In mixture designs the effects are given by traces (profiles) of predicted model values (which are not impacted by VIF) over the constrained mixture region. Indeed, effects of traditional DOE can also be shown be traces of predicted values (instead of model coefficients) which is what the prediction profile is. Hope this helps.

Re: Designing Mixture Experiments

Sammi_Chemist — Fri, 20 Mar 2026 08:37:13 GMT

A really informative presentation to share with the community. Thank you, Tom, and to the JMP team too.

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Designing Mixture Experiments

Re: Designing Mixture Experiments

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