Advanced Methods for Constructing UE(\(S^2 )\) Optimal Supersaturated Designs in Factor Screening Experiments

Supersaturated designs (SSDs) are crucial in factor screening experiments, especially when factor sparsity is assumed, meaning only a few factors are expected to be significant. Building on the foundational work of Jones and Majumdar [1], who introduced the UE(\(S^2 )\) criterion as an improvement over the E(\(S^2 )\) criterion by Booth and Cox [2], this study simplifies the construction of UE(\(S^2 )\) -optimal designs. The UE(\(S^2 )\) criterion is similar to the E(\(S^2 )\) criterion but removes the requirement for factor level balance. Our contribution lies in further simplifying these methods, explaining them with practical examples, and providing proofs for lower bounds for UE(\(S^2 )\) designs. Through this study, we aim to make the concepts and applications of supersaturated designs more accessible and easier to understand for practitioners. These methods can significantly optimize resource use and reduce costs in industrial, biological, and agricultural experiments. The study's implications extend to any field requiring efficient factor screening, offering a robust framework for future research.