Hi @Manistat,
I may have some questions to further help you :
- If I understand your goal, you would like to do a screening of process parameters to identify the ones that are significant on the outcomes of your process (so main effects screening) ?
- Why do you want a middle point for each factor range, are you expecting some curvature in the response/quadratic effects ?
- What is your limitation of 10 treatments "at a time" ? Is it a constraint similar to "10 runs per day" (equipment/experimental constraint)?
- What is your experimental budget in total (a multiple of 10 I guess) ?
- Do you have any restriction in the experimental space to consider (disallowed combinations like "If X1 is set at 1, then X2 can't be at -1") ?
- Do you have any restriction on treatments randomization to consider : a factor that is "hard to change" and you prefer to set it at a certain value for a certain number of runs before re-setting it ?
Depending on your responses, several designs may be possible (here done without any additional constraints) :
- A Custom design, with the 7 continuous factors and a blocking factor (10 runs per block), specifying a model with main effects and quadratic effects (which are set as "Necessary" by default but may also be set as "If Possible" to save some experimental runs) in order to have middle points for each factors ranges. This design might require 20 runs by default (2 blocks of 10 runs).
- A Definitive Screening design, with 7 continuous factors, the option "Add Blocks with center runs to estimate Quadratic Effects" checked with 3 blocks and 4 extra runs. This option might require 23 runs by default (1 block with 9 runs, 2 blocks with 7 runs each).
You can have a look at the two designs attached, and compare the designs with the platform DoE -> Design Diagnostics -> Compare Designs to see which one would be the most appropriate (in case of accordance with your experimental budget, no additional restriction/disallowed combinations, etc...)
I hope this first answer will help you,
Update: If your question is related to optimality criteria (D, A, I...), you might find this link useful : Optimality Criteria (jmp.com)
Historically, the D-optimality criterion is used for screening designs (focuses on precise estimates of the effects), but the A-optimality is also very interesting to consider (focuses on minimizing the sum of the variances of the parameters estimates, and you have more freedom to put more emphasis on certain effects, for example more emphasis on main effects than on quadratic effects).
I-optimality is about minimizing the average prediction variance over the design space, so it is more suited for response surface models (which might not be your case).
Victor GUILLER
L'Oréal Data & Analytics
"It is not unusual for a well-designed experiment to analyze itself" (Box, Hunter and Hunter)
