Proposing a New Method for the Construction of Optimal Pairwise Balanced Block Designs
0Proposing a New Method for the Construction of Optimal Pairwise Balanced Block Designs Based on 3n Symmetrical Factorial Design
Layman Abstract : This study focuses on Pairwise Balanced Block Designs (PBBD), which are special arrangements used in statistics and combinatorics to organize experiments efficiently. PBBD is important because it helps create other types of incomplete block designs, which are useful when testing multiple factors in an experiment.
The research introduces a new method to construct an Optimal PBBD using a mathematical approach called the 3n symmetrical factorial design. The proposed method meets key statistical efficiency standards known as A-Optimality, D-Optimality, and E-Optimality, ensuring that the design provides the most accurate and reliable results with minimal experimental effort.
A numerical example is provided to show how the method works, and the results confirm that the design is universally optimal, meaning it performs better than other existing methods. This study offers a useful tool for researchers working with experimental designs in various fields.
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Original Abstract : The concept of PBBD is merely the combinatorial interest in block designs. Because with the help of PBBD many other incomplete block designs can be constructed. This study proposed a new method for constructing Optimal Pairwise Balanced Block Design using the concept of 3n symmetrical factorial design has been proposed. The designs constructed using the proposed new method is satisfied A-Optimality, D-Optimality and E-Optimality criteria’s. The constructed method is illustrated with numerical example and the design is found to be universal optimal.
View Book: https://doi.org/10.9734/bpi/mcsru/v3/4358
#Block_design #incidence_matrix #balanced_design #pairwise_balanced_block_designs #concurrent_matrix