I have a question about a mixture design that I am working on. The experiment in question is looking at the effect of blending different types of fluids on material compatibility.
Factors
Fluid_1 treat rate - the fraction of fluid A - 0-100
Fluid_2 treat rate - the fraction of fluid B - 0-100
Fluid_1 type - categorical, two levels
Fluid_2 type - categorical, two levels
Response
swell - continuous
A complication in the design stage is that the type of fluid A used cannot have an effect on the response when Fluid_A treat rate is 0, the same is true for Fluid_B at 0 treat rate. I therefore set up the design to exclude Fluid_A and Fluid_B type unless crossed with the relevant treat rate factor. This is reasonable provided that the option to centre polynomials is unchecked when fitting the model. I also wanted to put in some restrictions so that eg only one Fluid_A type would be used at Fluid_A treat rate of <10. The two runs in the below table are essentially repeats, but JMP will not treat them as such, including restrictions avoids this.
Fluid_1_treat | Fluid_1 | Fluid_2 |
0 | A | A |
0 | B | A |
Such restrictions are not allowed in a mixture deisgn, however since this is only a two component mixture with A always depending on B I opted to exclude Fluid_2 treat rate and simply use the treat rate of Fluid_1 as the only continuous factor. I therefore end up with a design for the following model.
Fluid_1_treat
Fluid_1_treat x Fluid_1
Fluid_1_treat x Fluid_1_treat
Fluid_1_treat x Fluid_2
Fluid_1_treat x Fluid_1_treat x Fluid_1
When fitting this I can produce a good model, however it has the Fluid_1 type affecting the response at 0 treat rate (see prediction profiler 1), which is not physically possible. Also the treat rate at which there is no effect of the Fluid_1 type is 50% (see prediction profiler 2), which seems rather too round a number to be a real result.
Fitting it as a mixture I results in a more sensible model,
Fluid_1_treat (mixture)
Fluid_1_treat x Fluid_1
Fluid_1_treat x Fluid_2_treat
Fluid_1_treat x Fluid_2
Fluid_2_treat (mixture)
Fluid_1_treat x Fluid_2_treat x Fluid_1
However there are some quite high correlation coefficients when the final model effect (Fluid_1_treat x Fluid_2_treat x Fluid_1) is included. Augmenting the design is necessary to resolve this. Is this because having the two mixture factors in the model I effectively have an additional effect to fit, despite the fact that it is linearly dependent on the other mixture factor?
Obviously the simple solution is to do the extra runs for the mixture design, but can anyone help me understand the issues with the first model?
