Constant Block-Size with Constant Sum-Block Partially Balanced Incomplete Block Designs

Abstract

This chapter delves into the introduction, methodology, and application of Constant Block-Size with Constant Sum-Block Partially Balanced Incomplete Block Designs (CBS-CSB PBIBDs) as an innovative class of experimental designs. The study defines key concepts, including constant block-size, constant block-sum, and constant sum-block, and outlines conditions for implementing CBS-CSB PBIBDs. The research presents experimental designs for various scenarios, such as t = 21, k = 3; t = 15, k = 3; t = 27, k = 3, and illustrates their respective cases through line charts. Notably, the study demonstrates that as the number of replicates (r) increases, the efficiency factors also increase, and when r = 1, efficiency (E) equals 0. In conclusion, CBS-CSB PBIBDs emerge as a valuable tool for experimental prioritization, offering a new perspective on partially balanced incomplete block designs. The research highlights the significance of CBS-CSB PBIBDs across diverse fields of experimentation. The findings equip readers with the ability to define, design, and analyze experiments using CBS-CSB PBIBDs, while acknowledging challenges and limitations associated with this approach. This study contributes to the broader understanding of experimental design and provides a foundation for future research directions in this innovative field.