Some New Dimensions to Construct Economical Circular Weakly Balanced Neighbor Robust Designs

Neighbor-balanced designs are used in the experiments where the performance of a treatment is affected by the treatments applied to its neighboring units. These are well-known designs to balance the neighbor effects. Among these designs, minimal neighbor-balanced designs are economical; therefore, these are preferred by the experimenters. For v even, minimal neighbor balanced designs in circular blocks cannot be constructed for most of the cases, where v is number of treatments. In such situations, experimenters would like to relax the neighbor balance property up to some extent and consider the minimal circular weakly balanced neighbor designs as the better alternates to the minimal circular neighbor-balanced designs. In this article, some generators are developed to obtain minimal circular weakly balanced neighbor designs in blocks of equal, two and three different sizes.