In a customized design, if block factors are included in the factors and RSM (Response Surface Methodology) is incorporated into the model, how is the minimum number of experiments calculated?

[#1]

Hello, regarding the case where the number of experimental replicates is set to 2 and the minimum number of runs is 12, may I ask why the number of runs is not increased to avoid the occurrence of singularity? Is it acceptable for the design to remain singular?

[#2]

Hi @CompositeCamel5,

A singular design is indeed not recommended, as you won't be able to differentiate and estimate terms in your model.
However, it's not an impossible task if you follow the three principles behind the analysis of DoE : Effect Hierarchy, Effect Heredity and Effect Sparsity. You can start building your model with domain expertise and following these principles, starting with the identification of active main effects before including higher order terms to improve model performances and better respect regression model assumptions.

The pattern in the number of runs recommended by JMP is here a bit surprising, but I think this is a tradeoff (and manageable risk) of not increasing the design size from 12 to 18 for "just" one degree of freedom (information) missing. There are enough estimation methods and ways to deal with this situation, and effect sparsity principle should help you analyze such "supersaturated" situations, as not every effects will be important/significant.

Hope this answer will help you,