IJPAM: Volume 19, No. 1 (2005)


Bronis\law Ceranka$^1$, Ma\lgorzata Graczyk$^2$
$^{1,2}$Department of Mathematical and Statistical Methods
Agricultural University
Wojska Polskiego 28, Poznan, 60-637, POLAND
$^1$e-mail: bronicer@au.poznan.pl
$^2$e-mail: magra@au.poznan.pl

Abstract.The paper deals with the problem of estimation of individual weights of objects using the chemical balance weighing design. We assume that not all objects are included in each weighing operation. Addtionally we assume that the number of times in which each object is weighed is less then number of all measurement operations. The errors are correlated and they have equal variances. We give the lower bound of variance of each of the estimators and the sufficient and necessary conditions under which this lower bound is attained. The new construction methods for the optimum chemical balance weighing design are given. They are based on the incidence matrices of the balanced incomplete block designs and the ternary balanced block designs.

Received: September 3, 2004

AMS Subject Classification: 62K15

Key Words and Phrases: balanced incomplete block design, chemical balance weighing design, ternary balanced block design

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 1