Hi @dadawasozo,

The question about "default" number of runs is a frequent question on this forum. See an example here : : https://community.jmp.com/t5/Discussions/Plan-optimal-facteurs-cat%C3%A9goriels/m-p/643356#M83998

Short answer, you can find the reponse about the computed "Default" number of runs in the Custom Design platform here : Design Generation (jmp.com) : "*This value is based on heuristics for creating a balanced design with at least four runs more than the Minimum number of runs.*"

Depending on the type of factors you have and the model assumed, the default number of runs may change (for example depending on the number of odd-levels categorical factors) and may be more than minimum + 4 runs (if this resulting design is not balanced).

As a general understanding, default or recommended number of runs will always be higher than minimum number of runs. The minimum number of runs represents a saturated design : there are as many estimated parameters as there are observations. Each independent observation will create a degree of freedom, which is used to estimate an effect term in the model. In your case, you have 7 effects terms (3 main effects, 3 two factors interactions and 1 three factors interaction) and the intercept to estimate (so 8 parameters in the model), so the minimum number of runs required to fit this model is 8.

In order to have some degree of freedom left to calculate pure error (vs. model error) and assess model's quality and robustness through lack-of-fit test, JMP recommends "by default" an higher number of runs than the minimum number of runs, based on heuristics as seen before.

I hope this answer will help you,

Victor GUILLER

Scientific Expertise Engineer

L'Oréal - Data & Analytics