In Design of Experiments (DOE), what is the purpose of a factorial design?

In Design of Experiments (DOE), the purpose of a factorial design is to systematically investigate the effects of multiple factors (input variables) on a response (output variable) and, most importantly, to determine if there are any interactions between these factors. A factorial design involves testing all possible combinations of the factors at different levels. For example, if there are two factors, each at two levels (e.g., high and low), a full factorial design would require four experimental runs to test all four possible combinations. This allows you to not only determine the individual effect of each factor on the response but also to identify any interactions, where the effect of one factor depends on the level of another factor. Identifying these interactions is crucial for optimizing the process because it reveals synergistic or antagonistic effects that would be missed if each factor were studied independently. For instance, in 3D printing, a factorial design could be used to study the effects of layer height and printing speed on part strength and to determine if the effect of layer height on strength depends on the printing speed.