Hi @PYS,

I am wondering how adding a certain number of levels really help or support your objectives for this study and DoE ?

- Why does the client want additional levels ? Does he expect some curvature in the response, or other non-linear effects ? Does it correspond to levels frequently used ?

- If you're in a screening phase with 5+ continuous factors (as this seems to be the case since you're mentioning D-optimality), you may be interested in Definitive Screening Designs, efficient designs that can detect interaction and quadratic effects. This design will create 3 equally distant levels (coded -1, 0 and 1) for each continuous factors.
- You can also use Custom Design with continuous factors, and specify in the model higher order effects to "force" the design generation to introduce additional levels : for example, adding up to 2nd order term X4.X4 will create 3 levels for X4, up to 3rd order term X4.X4.X4 will create 4 levels in the design for X4, etc...

If you need to specify specific levels for this factor and these levels shouldn't be equidistant, then you can use Discrete Numeric factor and specify the appropriate terms in the model (JMP should do it by default with these terms specified as "If Possible).

Note that for the same runs number, increasing the number of levels for a factor decreases D-Efficiency, as the parameter estimates are less precisely estimated : instead of using runs only at -1 and +1 levels to estimate the slope of the effects for the response, you have more levels and less repetitions of these extreme levels, so the slope is less precisely estimated.

Hope this answer will help you,

Victor GUILLER

Scientific Expertise Engineer

L'Oréal - Data & Analytics