LATEST NEWS

International Journal of Modern Computation, Information and Communication Technology

ISSN 2581-5954

July-August 2020, Vol. 3, Issue 7-8, p. 56-63.​​

Relative Efficiency of Sum Constructed Automorphic Symmetric Balanced Incomplete Block Designs
C. W. Otulo, Z. M. Muga, N. B. Okelo, J. O. Nyakinda
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology.P.O. Box 210-40601, Bondo, Kenya.
*Corresponding author’s e-mail:
bnyaare@yahoo.com

Abstract

Several construction methods have been introduced to build the elements of BIBDs’ for specific parameters, with different techniques suggested for testing their existence, still no general technique to determine the efficiencies of these designs has been realized. In this study the efficiencies and relative efficiencies of Sum constructed automorphic symmetric balanced incomplete block designs with respect to parent designs has been presented. The process involved the classical analysis of variance applied to a data set. Computed relative efficiency of the design λ3 with respect to parent design λ1 has been found to be 1.216.

Keywords: Relative efficiency; Symmetric Balanced Incomplete Block Design; Automorphic Symmetric Balanced Incomplete Block Design.

References

  1. Alabi MA. Construction of Balanced Incomplete Block Design of Lattice Series I and II. International Journal of Innovative and Scientific and Engineering 2018; 16(4):10-22.
  2. Allan G. Some Open (And Some Closed) Questions On Symmetric BIBDs and PBIBD's", Annals of the New York Academy of Sciences, New York; 1979.
  3. Chan B, Eccleston A. On construction of complete and Partial Nearest Neighbor Balanced designs. Australasian J. Combinatorics 2017;8:39-50.
  4. Fisher R. An Introduction to Balanced Incomplete Block Designs, Combinatorial Designs, London; 1939.
  5. Kelechi AC. Symmetric and Unsymmetric Balanced Incomplete Block Designs: A Comparative Analysis. International Journal of Statistics and Applications 2012;2(4):33-39.
  6. Kumarland CS. Efficiency of Nearest Neighbor Balanced Block Designs for Second Order Correlated Error. Journal of mathematics 2017;13(1):62-71. 
  7. Otulo WC, Ojunga S, Otumba E. Screening New strains of sugarcane using Augmented Block Design. Mathematical theory and Modelling 2018;4(8):153-61.
  8. Parker ET. Remarks on Balanced Incomplete Block Designs. Proceedings of American Mathematical Society 2019;14(5):729-30.
  9. Parvathy S, Bury S. Final Report on Theory of Block Designs, Indian Institute of Science Education and Research Journal 2020;4(3):12-37.
  10. Rajarathinam A, Mahalakshmi S, Ghosh K. Construction of Efficiency Balanced Block Designs with Repeated Blocks. Int. J. Mathematical Statistics 2016;5(2):43-6.
  11. Sinha K, Das A, Dey A, Kageyama S. An Efficient Balanced Treatment Incomplete Block Designs. Australasian J. Combinatorics 2019;8:32-6.