Run orders in factorial designs using the assignment–expansion method

Abstract

In the practical application of experimental design, the run order significantly impacts the efficiency of the estimations and the associated costs. Recently proposed ordering methods for factorial designs have mainly focused on minimizing the number of level changes while maintaining low bias, as it has not been possible to minimize both properties simultaneously. This paper introduces the assignment–expansion method, which implements optimization techniques to adapt the assignment problem and obtain sequential orders with a limited number of runs, thereby reducing the bias and the number of level changes. Subsequently, the expansion method is employed to generalize the desirable properties to designs with a greater number of factors and levels. This method proved able to obtain orders for more general factorial designs that turned out to have the desired properties and simultaneously minimized the bias and the number of level changes. Furthermore, some of these orders achieved minimum values for both criteria.