Construction of 𝜶– Resolvable and nearly 𝜶– Resolvable BIB designs

Abstract

In experimental design, 𝛼-resolvable designs are preferred for their ability to partition blocks into subsets, each containing every treatment 𝛼 times. These designs offer advantages such as orthogonality to management effects, ensuring that such effects do not interfere with treatment assessments. Moreover, they provide protection against the loss of entire blocks, where all treatments are equally affected. Resolvable designs facilitate intra-block analysis of variance, breaking down the block sum of squares into replication and block-within-replication components, aiding in data interpretation. However, 𝛼-resolvable designs are not always feasible for all experimental parameters. In such cases, nearly 𝛼-resolvable designs, where blocks can be grouped into sets containing (𝑣−1) treatments 𝛼 times, offer a flexible alternative. These design concepts contribute significantly to experimental robustness, orthogonality, and variance analysis in various research contexts. In this article, we have developed a construction method of 𝛼-resolvable BIB designs for even number of treatments and a general construction method of nearly 𝛼-resolvable BIB designs.