DOE for Nested Factors

[#1]

Hello!  I'm designing an experiment with 5 factors.  Factor X1 is Ingredient Type, a two-level categorical variable (Ingredient A or Ingredient B).  But we also want to investigate the concentration of both ingredients.  Ingredient A has a range of 5% to 20%, while Ingredient B has a range of 1% to 10%.  I can't include this as three independent factors. 

I see two reasonable options:

- Run two sequential experiments.  First run a screening experiment with X1 as a two-level categorical variable, to find which Ingredient Type gives a better response.  Second, run an optimization experiment to investigate concentration of the better ingredient.

- Run one experiment, but make X1 a four-level categorical variable: A-high, A-low, B-high, B-low.

Two questions for the community: Which of these two options is better?  Is there a better option that I'm not thinking of?

Many thanks to the community!

[#2]

Chris,  There are some questions to think about:

1. Are you trying to understand causal structure or are you trying to find a "winning" recipe?

2. How much do you understand the noise (e.g., lot-to-lot variation of ingredients, measurement error, ambient conditions, mixing rate, etc.)?

3. Do you understand where the largest variation is in the output product (within batch, between batch)?  Is the variation consistent?

While I think sequential experimentation is the best approach in general, the dilemma of your first option is you may be comparing the 2 types at less than optimum conditions.  Your second option may not have the constraints you are concerned with (also looks like an OFAT).

You should look into mixture designs.

https://www.jmp.com/support/help/en/17.0/?os=mac&source=application#page/jmp/mixture-designs.shtml#

[#3]

Hello @chris_rigdon,

Are the experiments not measurable when ingredient A is in the range 1-5% and B in the range 10-20% ?

Some other questions related to your design and other factors :

• What are the other factors types ?
• What is your objective ?
• Which kind of design or model do you want to investigate ?
• Are there any other constraints in your design (other ingredients in the formulation with a constraint on the total sum/ratio ?) ?

If there is a "technical" reason for this difference in scale, there may be a solution by using "Custom Design", and then specifying "Disallowed combinations" :

1. You create a 2-levels categorical factor for ingredient, and a continuous factor for concentration (from 1 to 20).
2. Then, in the disallowed combination filter, you choose your factor and levels for which there should not be a single experiment in this space : 

Or you can use this script in the "Disallowed Combinations Script" :

Ingredient type == "A" & Concentration <= 5 | Ingredient type == "B" & Concentration >= 10

Then the design creation should take into account these constraints and avoid creating points in the excluded area (here a small example only with these 2 factors):

This may be a technical solution, but as @statman writes, there are several questions to consider before creating a design.

Hope this may help,