Orthogonal Arrays and Row-Column and Block Designs for CDC Systems

Volume 1 - Issue 1

Mahndra Kumar Sharma* and Mekonnen Tadesse

Received: September 06, 2018;   Published: September 20, 2018

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Summary

In this article, block and row-column designs for genetic crosses such as Complete diallel cross system using orthogonal arrays (p2, r, p, 2), where p is prime or a power of prime and semi balanced arrays (p(p-1)/2, p, p, 2), where p is a prime or power of an odd prime, are derived. The block designs and row-column designs for Griffing’s methods A and B are found to be A-optimal and the block designs for Griffing’s methods C and D are found to be universally optimal in the sense of Kiefer. The derived block and rowcolumn designs for method A and C are new and consume minimum experimental units. According to Gupta block designs for Griffing’s methods A,B,C and D are orthogonally blocked designs. AMS classification: 62K05.

Keywords: Orthogonal Array; Semi-balanced Array; Complete diallel Cross; Row-Column Design; Optimality

Abstract| Introduction| Model and Estimation in 1-Way Heterogeneity Setting| Model and Estimation in 2-Way Heterogeneity Setting| Relation between Orthogonal Array (p2, p+1, p, 2) and Designs for CDC System| Relation between Semi-Balanced Array (p(p-1)/2, p, p, 2) and Designs for CDC System| Conclusion| References|