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

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMPS_2004_24_2_a3,
     author = {Ceranka, Bronis{\l}aw and Graczyk, Ma{\l}gorzata},
     title = {Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {215--232},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2004_24_2_a3/}
}
TY  - JOUR
AU  - Ceranka, Bronisław
AU  - Graczyk, Małgorzata
TI  - Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2004
SP  - 215
EP  - 232
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2004_24_2_a3/
LA  - en
ID  - DMPS_2004_24_2_a3
ER  - 
%0 Journal Article
%A Ceranka, Bronisław
%A Graczyk, Małgorzata
%T Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors
%J Discussiones Mathematicae. Probability and Statistics
%D 2004
%P 215-232
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2004_24_2_a3/
%G en
%F DMPS_2004_24_2_a3
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/