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Functional DOE to optimise single peak shape AND position

Hi,

A JMP Pro user is interested in using FDOE to optimise a Cell Assay.

Each run produces a signal vs time curve with one peak. The shape AND position of the curve is dependent on the factors. The goal is to find factor conditions to achieve a sharp peak at 17 hours.

Possible cell assay curves (left) and optimal (right)Possible cell assay curves (left) and optimal (right)

I am thinking this will require DTW to align the peaks and then FDE should be able to model different curve shapes. But then we will need to model the DTW shift against the factors to find out how to optimise.