# How to extend Plackett-Burman design to further explore the interactions?

Cross Validated Asked by NoThanks93330 on January 1, 2022

My situation is as follows: I have built a 2-level Plackett-Burman design with 10 factors (some are actual 0/1-variables, the others are numeric and I used the minimum and the maximum) and 32 experiments. The experiments are done, the results are at hand and the resulting (linear) models are ok but not quite satisfying.

So far those models only contain main effects and no interactions, because in the current design with 10 factors in 32 experiments the interactions are highly correlated und therefore using them in the models would not give meaningful results (right?).

The assumption now is that it’s probably the interactions, which are missing to make satisfying models, and to explore them I need to do more experiments. But what kind of design should I use here? My best guess so far is extending the 2-level design to a (face-centered) central composite design, because it’s said to be for "exploring non-linear effects". So is this the way to go or are there better methods?

edit: context is a plc controlled machine in which we are trying to detect whether or not the outcome of a production cycle (i.e. the product) will be satisfying or not. So the factors we are changing in the experiments are different machine settings and differences in the processed workpieces that influence the production process and the outcome.

That might be a good way to go, but (depending on context you did not tell) it might be wise to run the new points as a new block$$^dagger$$. Another way of extending the design might be to use software for optimal design, also called algorithmic design (D-optimality, search this site).

Then you would have to define a set of candidate points, and the software will choose among them. Going that way, be sure to use more than two experimental points (among the candidate points) for the continuous variables (maybe the extremes + at least the center point), and quadratic effects + interactions in the model, so you get a design that can actually detect nonlinearities.

$$^dagger$$This means to make a categorical variable (factor, in R-speak) with values old run, new run (possibly more) and include that in the analysis. That accounts for possible change in conditions between the runs.

Answered by kjetil b halvorsen on January 1, 2022