Discussiones Mathematicae Probability and Statistics 24(2) (2004) 215-232

OPTIMUM CHEMICAL BALANCE WEIGHING DESIGNS WITH DIAGONAL VARIANCE - COVARIANCE MATRIX OF ERRORS

Bronisław Ceranka and Małgorzata Graczyk

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

Abstract

In this paper we study the estimation problem of individual measurements (weights) of objects in a model of chemical balance weighing design with diagonal variance - covariance matrix of errors under the restriction k1 + k2 < p, where k1 and k2 represent the number of objects placed on the right and left pans, respectively. We want all variances of estimated measurments to be equal and attaining their lower bound. We give a necessary and sufficient condition under which this lower bound is attained by the variance of each of the estimated measurements. To construct the design matrix X of the considered optimum chemical balance weighing design we use the incidence matrices of balanced bipartite weighing designs.

Keywords: balanced bipartite weighing design, chemical balanceweighing design.

2000 Mathematics Subject Classification: 62K15.

References

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Received 10 February 2004
Revised 4 August 2004