A bakery experiment

In 2023, a company producing bakery products contacted KU Leuven for an extensive experimental design. One controllable factor indicated 3 types of flour. Further, 14 controllable factors were related to concentrations of ingredients and 2 were time-related. So there were 16 quantitative factors. All of these had to be studied at three levels.

Regarding the two-factor interactions, most of the interest was for the linear by linear interactions of the quantitative factors, and the interactions between the flour factor and the linear effects of the quantitative factors.

This situation called for a screening design. Definitive Screening Designs for quantitative factors are not good in detecting quadratic effects, because they have a very limited number of runs at the middle level of the factors. Instead, I derived my design from a regular three-level design with 18 factors and 243 runs. I used one of the factors to split the design in three blocks. One of the blocks  is not used. In the design based on the other two blocks, I selected the best option for the qualitative factor. For each of the 16 qualitative factors, I searched for the best way to turn its three levels, l1, l2 and l3, say, into -1, 0 and +1. The illustration shows the final design.