Discussiones Mathematicae Probability and Statistics 21(2) (2001) 99-110

SOME OBSERVATIONS ON THE CONSTRUCTIONS OF CHEMICAL BALANCE WEIGHING DESIGNS

Ratnakaram Nava Mohan

D. A. R. Department of Mathematics, College,
Nuzvid-521201, A.P., India

e-mail: rnmohan@hotmail.com

Bronisław Ceranka

Department of Mathematical and Statistical Methods
Agricultural University of Poznań
Wojska Polskiego 28, 60-637 Poznań, Poland
e-mail:
bronicer@au.poznan.pl

Sanpei Kageyama

Department of Mathematics, Graduate School of Education
Hiroshima University, Higashi-Hiroshima 739-8524, Japan
e-mail:
ksanpei@hiroshima-u.ac.jp

Abstract

The construction of some optimum chemical balance weighing designs from affine μ-resolvable balanced incomplete block (BIB) designs are discussed in the light of a characterization theorem on the parameters of affine μ-resolvable BIB designs as given by Mohan and Kageyama (1982), for the sake of practical use of researchers who need some selective designs for the construction of chemical balance weighing designs.

Keywords: optimum chemical balance weighing design; BIB design; ARBIB design; μ-ARBIB design.

2000 Mathematics Subject Classification: Primary 05B05; Secondary 62K10.

References

[1] M. Bhaskararao, Weighing designs when n is odd, Ann. Math. Statist. 37 (1966), 1371-1381.
[2] R.C. Bose, A note on the resolvability of balanced incomplete block designs, Sankhya 6 (1942), 105-110.
[3] B. Ceranka and K. Katulska, A relation between BIB designs and chemical balance weighing designs, Statist. & Prob. Lett. 5 (1987), 339-341.
[4] A. Dey, On some chemical balance weighing designs, Austral. J. Statist. 13 (1970), 131-141.
[5] S. Kageyama and R.N. Mohan, Constructions of α-resolvable PBIB designs, Calcutta Statist. Assoc. Bull. 34 (1980), 221-224.
[6] S. Kageyama and R.N. Mohan, On μ-resolvable BIB designs, Discrete Math. 45 (1983), 113-122.
[7] S. Kageyama and G.M. Saha, Note on the construction of optimum chemical balance weighing designs, Ann. Inst. Statist. Math., Part A 35 (1983), 447-452.
[8] R.N. Mohan and S. Kageyama, On a characterization of affine μ-resolvable BIB designs, Utilitas Math. 22 (1982),17-23.
[9] A.K. Nigam, A note on optimum chemical balance weighing designs, Austral. J. Statist. 16 (1974), 50-52.
[10] D. Raghavarao, Some optimum weighing deigns, Ann. Math. Statist. 30 (1959), 295-303.
[11] D. Raghavarao, Some aspects of weighing deigns, Ann. Math. Statist. 31, (1960), 878-884.
[12] D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments, Dover, New York 1988.
[13] G.M. Saha, A note on relation between incomplete block and weighing designs, Ann. Inst. Statist. Math. 27 (1975), 387-390.

Received 10 November 2001