On Complete Diallel Cross Plans

Authors

  • Maengseok Noh Major of Bigdata Convergence, Pukyong National University, Busan, South Korea
  • D. K. Ghosh Department of Statistics, Saurashtra University, Rajkot, India
  • Poonam Singh Department of Statistics, University of Delhi, Delhi, India
  • Nilesh Kumar School of Business, UPES, Dehradun-248007, India

DOI:

https://doi.org/10.13052/jrss0974-8024.1922

Keywords:

BIB design, CDC plan, GCA, optimality, efficiency

Abstract

A diallel cross is a pairing strategy commonly employed by animal husbandry scientists and botanists to explore the genetic interactions and inheritance patterns among a set of l inbred lines. A commonly used diallel cross design is a complete diallel cross (CDC) plan where each line is crossed with the remaining (l−1) distinct lines, resulting in l(l−1)/2 number of crosses in the entire design.

In this investigation, we present a method for constructing complete diallel cross schemes based on balanced incomplete block design (BIBD) of series t=b=l,r=k=l−1, and λ=l−2. Here, crosses are made in such a way that one line will cross with other line within a block. Two methods viz, (i) binary complete diallel cross plan and (ii) non-binary CDC plans are developed from the same series of BIBD to suggest which plans should be accepted by the breeder for their experiment. The construction of CDC plan is demonstrated though appropriate examples. We compute the efficiency of the CDC plan and compare it with randomized complete block design. It is shown that the constructed CDC plan is universally optimal. Robustness of CDC plan is examined in relation to the loss of one block.

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Author Biographies

Maengseok Noh, Major of Bigdata Convergence, Pukyong National University, Busan, South Korea

Maengseok Noh received the B.S., M.S. and Ph.D. degrees from the Department of Statistics, Seoul National University, in 1996, 1998 and 2005, respectively. His thesis was on analysis of binary data and robust modelling via hierarchical likelihood. Since 2006, he has been a Professor with Department of Statistics, Pukyong National University, Busan, Korea. His current research interests are application and software developments for hierarchical generalized linear models, development of methodology for zero-inflated Poisson model with spatial correlation and hierarchical approach non-Gaussian factor analysis.

D. K. Ghosh, Department of Statistics, Saurashtra University, Rajkot, India

D. K. Ghosh did his Ph.D. in Design of Experiments under the supervision of Professor M. N. Das from ISI Delhi, India. He retired as Professor and Head, department of Statistics from Saurashtra University fourteen years back. He received the highest recognition from UGC New Delhi as Basic Science Research (BSR) Faculty Fellow after superannuation. Recently he was awarded lifetime achievement award. He is a Fellow of Royal Statistical Society, ISPS and GSA. He has credit of supervising forty-three Ph.D. students in Design of experiments, Inference, Operations research, Biostatistics and Management and published more than 150 research paper in reputed National and International journals. He has published eight books as co-authors and several book chapters. He visited the west Florida University, Pensacola, USA and University of Manitoba, Winnipeg, Canada number of times as research collaborator and published good number of papers as co-authors. He is a member of eleven professional body. He is Associate editor and member of editorial body for few journals. He is also the Editor in Chief of Gujarat journal of Statistics and Data Science.

Poonam Singh, Department of Statistics, University of Delhi, Delhi, India

Poonam Singh is the Senior Professor & Former Head of the Department, Department of Statistics, University of Delhi, Delhi, India. She has more than thirty-two years of academic and research experience. Her areas of research mainly include design of experiments, linear models, and generalized linear models. She has published seventy-four research papers in reputed national and international journals and five book chapters. She has a credit of supervising twelve Ph.D. and thirteen M.Phil. students. Her fields of interest and specialisation are design of experiments, linear models, generalized linear models, optimization, econometrics, regression analysis, statistical quality control and operations research.

Nilesh Kumar, School of Business, UPES, Dehradun-248007, India

Nilesh Kumar received his M.Phil. and Ph.D. in statistics (with specialization in Design of Experiments) from Department of Statistics, University of Delhi, India. He is currently serving an Assistant professor-senior scale at School of Business, UPES, Dehradun, India. Prior to this, he was working as a Research Professor at Pukyong National University, South Korea. His area of research includes design of experiments, computer experiments and development of AI/ML algorithms.

References

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Published

2026-06-16

How to Cite

Noh, M. ., Ghosh, D. K. ., Singh, P. ., & Kumar, N. . (2026). On Complete Diallel Cross Plans. Journal of Reliability and Statistical Studies, 19(02), 263–284. https://doi.org/10.13052/jrss0974-8024.1922

Issue

2026: Vol 19 Iss 2

Section

Articles