Construction of PBIB Designs by Using Boolean Algebra

Singh, Gurinder Pal; Garg, Davinder Kumar

doi:10.29055/jcms/731

JCMS

2018

DOI: 10.29055/jcms/731

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Construction of PBIB Designs by Using Boolean Algebra

Gurinder Pal Singh¹,

Davinder Kumar Garg²

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2024

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

L. Adeleke,

O. Adebayo,

A. Osuolale

2024

Response Surface Methods - Theory, Applications and Optimization Techniques

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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.

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

L. Adeleke,

O. Adebayo,

A. Osuolale

2024

Response Surface Methods - Theory, Applications and Optimization Techniques

View full text Add to dashboard Cite

show abstract

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Construction of PBIB Designs by Using Boolean Algebra

Cited by 1 publication

References 0 publications

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

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

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