Best design for ingredients with category caps

[#1]

I have to design an experiment involving 1 fixed ingredient (A), 1 ingredient with a minimum and maximum % to use (B) and ingredients from 9 other different categories (C to K).

Each category from C to K have varying number of ingredients within those categories, varying from atleast 2 to a maximum of 9. And each of the ingredients in these categories have a recommended use level (%), so it is either present at that level or not present at all in a particular run. 

There is only 1 response variable which needs to be maximised.

The maximum number of runs which is practically feasible to run is 100.

Here is an example:

• A - always present at 4%
• B - concentration between 50-70%
• C - Maximum concentration should be 10%
  • C1 - either absent or present at 5%
  • C2 - either absent or present at 5%
  • C3 - either absent or present at 2%
  • C4 - either absent or present at 3%
• Other categories similar to C

What is the best way to design such an experiment in JMP? And are there any limitations with regard to the computational power of the PC being used?

[#2]

I'll start my thoughts with the answer to your last question. Yes there are limits with regard to the computational power of the PC being used. For JMP system requirements I suggest reading here: JMP System Requirements Some of this is also predicated on the version of JMP you are using. In general, these requirements are either binary (must have for JMP to function at all) or 'the more the merrier', with some recommended minimum, such as RAM. There is a highly recommended minimum...but if you've got more, JMP will perform faster, with fewer headaches for the user.

Now some general thoughts on '...the best way to design such an experiment in JMP?' question:

1. What is the overall goal of the problem at hand? Screening 'categories' which I'll call factors from here on out? Optimizing the response? Maybe if it's both start with a screening style experiment...then move sequentially to optimization type experimentation?

2. Are there restrictions on randomization over and above those you've articulated?

3. Are the factors continuous? And does placing any factor at 'absent' make the whole system behave in a way that is atypical wrt to the response? In my experience with chemical based systems in experimentation sometimes complete absence induces a very nonlinear effect (think step change as an example) in the response for the factor, making modeling for optimization purposes more problematic.

4. Is this truly a DOE mixture experiment where the sum of the factor levels must equal 100%?

5. This is clearly a problem for JMP's Custom Design platform...so in general I think you'll start there.

[#3]

Hi,

Thanks for your reply. So here are some clarifications corresponding to your comments:

• the overall goal is to find the best combination of ingredients that would maximize the response variable
• the category caps and the use-level of the ingredients are the only restrictions. There are no other randomization restrictions
• the factor levels can be either 0 or the use-level prescribed. So I believe they are continuous variables (please correct me if I am wrong here). One of the ingredients being absent (i.e. factor level 0) is not going to make the whole system behave in a way that is atypical wrt to the response since there is a fixed level of one or two ingredients (A and B from the example) always present. All the other ingredients within the categories are optional.
• Yes, the sum of the factor levels must add up to 100.

I had actually started with a custom design having a mixture variable for B, a constant for A and continuous (two-level) variables for the ingredients within each category. But adding linear constraints on that seemed very complex.

[#4]

Hi,

In addition to the comments from @P_Bartell, this sounds as though it could be a Mixture of Mixtures design.  You can find information on how to construct those here: Mixture of Mixtures Design (jmp.com).

[#5]

Hi,

Thanks for your reply. 

This was my initial thought as well when I browsed through the JMP examples in the documentation. What I found difficult to articulate here was that my ingredients can take only two values (either 0 or the use-level) rather than a range of values within a lower and upper limit as in a normal mixture variable. 

How do I include such a case in a mixture of mixture design?

[#6]

Hi,

If the factors can only take on two values and non in the middle, it may be better to consider them categorical variables.  These can be added easily in Custom Design as well (https://www.jmp.com/support/help/en/16.2/#page/jmp/factors.shtml#).

[#7]

Hi,

If I define the ingredients within each category as categorical variables with two levels, it wouldn't be possible to specify the category caps as constraints right? 

From the example in the question, if C1,C2,C3 and C4 are categorical variables as follows:

C1 = 0,5

C2=0,5

C3=0,2

C4=0,3

How would i describe a constraint to say that C1+C2+C3+C4 < 10 ? As far as I understand, I can only add linear constraints to either continuous or mixture variables.