DoE Optimise a ratio of two factors

Question

I currently have a material made using 100% of expensive factor A. I want to replace some of A with cheaper factor B but I'm not sure what the optimal ratio would be to achieve the same performance when using 100% of factor A. I believe I need a minimum of 50% factor A.

How could I design a series of experiments using JMP (pro 18) that try to optimise this ratio so I can remove most of the expensive factor A without effecting the performance. I have time to do 5 experiments.

I have tried using a mixture design but was only getting ratios of 100/0, 75,25 & 50/50 % when in reality I would like to do at least 1 experiment closer to 60/40.

Depending on the results I would also like to augment the design to optimise further, potentially looking at anywhere between 0-100% of factor A.

Thank you!

statman · Answer

There is not enough context to provide specific advice.

I have some questions/comments:

1. What are the response variables?  You suggest one is a "measure of performance".  We live in a multivariate world, so what are the other Y's?  For example, cost is another Y.

2. Have you studied your measurements systems?

3. How do you determine the consistency of either "A" or "B"?  Have you studied the lot-to-lot or batch-to-batch variation of either component?  Obviously you will have to take a sample for your experiments.  How representative will your sample be of future material?

4. What are the scientific or engineering hypotheses/theories?  What is actually different between "A" and "B"? Are the differences measurable?  Why is B cheaper?  Are there no other factors?  How is the material made?  Is there any time, temperature, etc. in making the product?  What noise might affect the product?

IMHO, you really aren't designing experiments per se.  You want to run 5 possible combinations and pick the best results from those 5.

Victor_G · Answer

Hi,

You can create manually your table, with rows as the individual experiments, a column to fill the ratio A:B and as much columns as responses you have. The ratios may be equidistant, so if you can afford 5 experiments you can create 5 values for A:B ratio like 1-0,75-0,5-0,25-0.
If you want to create it more easily (and automatically), you can use the Custom Design platform, specify one continuous factor ("ratio A:B", range from 0 to 1), and specify a model containing main effect and higher order terms (up to the 4th order if you want to generate 5 experiments for example) :

Once you have generated this simple design you can fill the response(s) and a script "Fit Model" will enable you to fit the polynomial model on the response(s) you have assumed during design creation.
Please find attached the datatable generated.

Hope this answer will help you,

Simple-ratio-design.jmp

DeepDormouse199 · Answer

Hi Victor,

That sounds really good. However, I am a beginner at using JMP and I am not sure how to do that using the software.

Thanks!