I have a slightly more conceptual question regarding DOE choice (or another experimental framework) when the effect of factors is non-linear. My experiment has many factors >10, which I reduced to 6, and ran a definitive screening design. Per the results (see image below), there is no clear linear relationship (or even quadratic) between the factors and outputs. Sure a few look like they can be, but generally it doesn’t look like so (at least per my analysis).
Based on this, my question is if the underlying response is non-linear does it even make sense to use/design a fractional factorial or definitive screening design (DSD), which can only go up to quadratic if I am not wrong, for the purpose of screening? If the goal is to screen, what other alternatives are there in the DOE toolbox that you recommend I should consider?
One solution I thought of was to decrease the range of each of the factors: the idea behind being that if you decrease the range small enough, then any underlying function/response will be linear. However, I might loose the point of the screening experiment, and I might have to conduct many screening experiments at different ranges. Is this what is done in practice with non-linear response? Consider the following graph I read in a paper. If the underlying response looks like this, I am not sure which DOE methods (initial screening + response surface?) can get me to something like this. What would be your recommendation on methods to find the global optimal in these cases?
