Geodesic
Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors
Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 2, pp. 215-232.

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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 
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Ceranka, Bronisław; Graczyk, Małgorzata. Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors. Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 2, pp. 215-232. http://geodesic.mathdoc.fr/item/DMPS_2004_24_2_a3/

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