Ordering factorial experiments

In many practical experiments, both the level combinations of factors and the addition orders will affect the responses. However, virtually no construction methods have been provided for such experimental designs. This paper focuses on such experiments, introduces a new type of design called the ordering factorial design, and proposes the nominal main effect component-position model and interaction-main effect component-position model. To obtain efficient fractional designs, we provide some deterministic construction methods. The resulting designs are D-optimal, and the run sizes are much smaller than that of the full designs. Moreover, in some cases, some constructed designs are still D-optimal after reducing the number of components and factors.