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Level I

## How to design a DOE covering 3 systems, 8 factors and 6 products resulting in one optimal setting?

I'm designing a DOE design with 7 variables that are all continuous. My expectation is 2 of these factors will probably have an optimum curve that is not linear, I also expect interactions between my variables.

I have 3pc of the system I'm testing on and my system needs to be able to handle 6 different products - my problem is that I need to find one compromise in settings that provide the optimal output of all 6 different products.

My idea is to design the DOE with the 3pc of the system as a categorical factor and the 7 variables as continuous factors. I'm hoping the system will not have an effect, but it might have and I need to have the same settings on all 3 systems. I will then perform the full DOE on all 6 products and try to find the optimal settings for a combination of all 6 products.

Does this design make sense to you, or do you have other suggestions? Would it be okay to only test at two levels for all 7 variables or do I have to test at 3 or more levels for the variables I do not expect to have linear behavior?

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Level VI

## Re: How to design a DOE covering 3 systems, 8 factors and 6 products resulting in one optimal setting?

Welcome to the community and JMP.

My questions and thoughts.  There are many options.

1. Design multiple plans (e.g., fractional factorial res IV, DSD, Fractional factorial with center points) predict all possible outcomes from each plan and resources required.  Also consider the first experiment is to design a better experiment, so you don't have to understand everything in the first iteration (e.g., non-linear effects).

2. I am confused by "3pc of the system".  I don't understand this? Is the system the measurement system? Without understanding this better, I don't really have any advice for you other than to identify why the 3pc are different and could you choose 2 of those and infer about the third?

3. There is no mention of response variables.  How many are there?

4. A thought, what if you consider "products" as noise and block on product (you could confound system in the block as well).  Select products you hypothesize to have the greatest differences and run those 2 blocks first.  You are not worried so much about block effects, but are looking for block-by-factor interactions which are indications that the effect of the variables in the experiment depend on which product you are using.  This is not the outcome you want, but you want to identify these effects early so the design can be changed to accommodate.

5. I would start with 2-level screening designs and augment those as you get closer to what you want. Complex models tend to work in small design spaces.  In reality, there is probably no such thing as a true linear relationship, but you are trying to approximate the complex surface with as simple a model as possible.

6. Consider the noise, how will you handle it? This is, in my experience, the most neglected part of experiment design.  It is however one of the most important aspects.  You want your design (and the conclusions from the analysis) to be representative of the future.  You should be careful not to restrict the noise as this negatively impacts inference space.  The challenge is, as the noise becomes closer to reality, the precision for detecting factor effects diminishes. So you will need strategies to handle the noise in the experiment (e.g., repeats, CRR, RCBD, BIB, split-plots).

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