Prioritization of the balancing property and full estimability in mixed-level designs

In a recently published work, a new class of Balanced Asymmetrical Nearly Orthogonal Designs (BANOD2) was proposed, which can simultaneously estimate both first and second order effects of all factors, with a limited run size. The motivation for the new class lies in using the balancing property as a necessary precondition for several practical concerns arising in the experimentation field. A balanced design optimizes the use of experimental resources in technological experiments, may avoid misinterpretations in choice experiments of marketing research, and can relieve the experimenter from the arbitrariness in assigning the levels to factors. Furthermore the balancing property assures the minimum variance of first-order effect estimates. The BANOD2 designs have also the important characteristic of allowing for the estimation of all main effects and two-factor interactions in mixed-level experiments. In this work the optimality properties of this class of designs are reviewed and comparisons with other classes of competing designs prioritizing other statistical properties (e.g. D- and E-optimality, and projectivity) are stressed. Examples of application in several industry and service sectors are illustrated and a software interface for their generation, based on a heuristic algorithm, is provided.