The design and analysis of order-of-addition experiments: An introduction and case study

We introduce order-of-addition (OofA) experiments, which study the order in which m components are applied, such as the order in which m chemicals are added to a mix or m layers to a film. We discuss a way for designing such experiments using the traditional paradigm of factors. A full design with m components requires m! runs, but we show that optimal or near-optimal experimental designs can be created with far fewer runs for the important practical cases of m=4, 5, 6, 7. An analysis method for OofA experiments is explained and is then illustrated with a case study of three sequential experiments.