A wood construction experiment
In 2010, I collaborated with people involved in strengthening wood constructions. Experimental factors often had more than two levels. One particular project was devoted to finding factors that might strengthen the wood-glue-wood bond. The picture shows a device to measure the strength. There were four different glues, three different kinds of wood, and four two-level processing factors. Happily, at that time I was also doing research on multilevel orthogonal arrays that could be used as experimental designs at Eindhoven University of Technology. One of the series we generated there had precisely these factors, while only 48 out of the 192 possible combinations were included in the designs.
The D-efficiencies of the designs with respect to a model with all the main effects and all the two-factor interactions.
There were 19 different designs such that main effect estimates of the factors are not affected by active two-factor interactions. Fourteen permitted the estimation of a model with all the main effects and all the two-factor interactions. I took the one with the highest D-efficiency for that model.
The design has a strength of 3, meaning that, for every set of 3 factors, all combinations occur equally often. It is interesting to consider what the advantage of the chosen design is over designs with a better D-efficiency but a smaller strength. I wrote an award winning paper on this subject; see Schoen (2010).