Adding Axial and Centroid Runs to Simplex Lattice and Centroid Designs

[#1]

Hi, does JMP support augmenting simplex lattice and centroid designs with axial and centroid points? I noticed that when I augment a simplex lattice design the 'axial runs' augmentation is disabled. In JMP documentations I have scanned thru it seems like JMP is only allowing an axial run augmentation if a screening design was used?

[#2]

Hi @BryanG ,

I had not come across the idea of axial points for mixture designs. From a quick search I found that an axial point is a mixture that is half-way between the centre-point and a vertex of the mixture space.

I am not aware of anyone recommending an approach of augmenting simplex lattice or simplex centroid designs with axial points as part of sequential experimentation. I don't think it would be a bad idea necessarily. But just not the best way to do things.

The recommended approach in JMP is optimal augmentation. That is, JMP will find the additional runs that are optimal to test the model that you have defined. You define the factors, factor ranges, model to estimate, and number of additional runs. Then JMP gives you the optimal additional runs.

Axial run augmentation is an option for designs with continuous (not mixture) factors. But it is really there for people that were taught the conventional (pre-computer) DOE methods.

As a workaround, you could create the ABCD design (DOE > Classical > Mixture Design) as this will contain the axial points. You can then copy them and add them to your existing design.

I hope this all helps,

Phil

[#3]

Hi @BryanG,

@Phil_Kayalready provided you good advices and infos on how to do it.

From my perspective (or at least it was how I have been taught, and maybe it's the same for you), axial points were traditionally used in Simplex Centroid Design for validating a model : you first used these points as validation points of your model to assess precision and variance of your predicted response values. In case of strong deviation between predicted vs. measured responses, you can then use these points to augment the design, improve the model's precision, and increase model complexity to Scheffé Cubic model for example.

This is the traditional approach I used in a previous presentation using Mixture Design and Functional Data Explorer : https://community.jmp.com/t5/Discovery-Summit-Europe-2021/Use-of-Functional-Data-Explorer-in-a-Mixtu...

But as Phil mentions, with the rise of advanced software and computational ressources, there are now equal or better options than this traditional one.

Hope my answer will help to understand the context,