Efficient and robust block designs for order-of-addition experiments

Designs for Order-of-Addition (OofA) experiments have received growing attention due to their impact on responses based on the sequence of component addition. In certain cases, these experiments involve heterogeneous groups of units, which necessitates the use of blocking to manage variation effects. Despite this, the exploration of block OofA designs remains limited in the literature. As experiments become increasingly complex, addressing this gap is essential to ensure that the designs accurately reflect the effects of the addition sequence and effectively handle the associated variability. Motivated by this, the study seeks to address the gap by expanding the indicator function framework for block OofA designs. The word length pattern is proposed as a criterion for selecting robust block OofA designs. To improve search efficiency and reduce computational demands, an algorithm is developed that employ orthogonal Latin squares for design construction and selection, thereby minimizing the need for exhaustive searches. The analysis, supported by correlation plots, reveals that the algorithms effectively manage confounding and aliasing between effects. Additionally, simulation studies indicate that designs based on the proposed criterion and algorithms achieve power and type I error rates comparable to those of full block OofA designs. This approach offers a practical and efficient method for constructing block OofA designs and may provide valuable insights for future research and applications.