Design for order‐of‐addition experiments with two‐level components

Abstract The statistical design for order‐of‐addition (OofA) experiments has received much recent interest as its potential in determining the optimal sequence of multiple components, for example, the optimal sequence of drug administration for disease treatment. The traditional OofA experiments focus mainly on the sequence effects of components, that is, the experimenters fix the factor level of each component and observe how the response is affected by varying the sequences of components. However, the components may also have factorial effects in that changing their factor levels in a given sequence can affect the response. In view of this, we consider the design problem for OofA experiments where each component is experimented at two levels. A systematic method is given to construct OofA designs that jointly considers the sequence design and factorial design for all components. By appropriately choosing the sequence and factorial designs, we show that the combination of the two parts results in a balanced design with an economical run size. Moreover, the constructed designs enjoy a number of optimality properties such as ‐, ‐ and ‐optimalities under some empirical models. The design method proposed can be extended to some other practical situations like the number of process variables is different from the number of components, and OofA experiments with multilevel components.