Small Mixed‐Level Orthogonal Designs

Screening designs are widely used to identify active effects from a large number of potential factors, ideally with a relatively small number of runs. This process is typically conducted in the early stages of experimentation. Orthogonal designs (ODs) are preferred because they allow the estimated main effects to remain uncorrelated. While two‐level and three‐level ODs have been extensively studied, ODs for mixed‐level experiments have received less attention. This is an important and timely issue, as mixed‐level experiments are common in practical applications. This paper proposes a new class of small mixed‐level ODs. These designs ensure the uncorrelated estimation of main effects and minimize run size among all ODs for a given number of factors. Additionally, the proposed designs exhibit favorable confounding patterns between main effects and two‐factor interactions, with each main effect being orthogonal to most two‐factor interactions. The construction methods leverage Paley's conference matrices. This research fills a critical gap in the literature by introducing new theoretical developments for mixed‐level experiments.