Geodesic
Optimum chemical balance weighing designs under the restriction on weighings
Discussiones Mathematicae. Probability and Statistics, Tome 21 (2001) no. 2, pp. 111-120.

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The paper deals with the problem of estimating individual weights of objects, using a chemical balance weighing design under the restriction on the number in which each object is weighed. A lower bound for the variance of each of the estimated weights from this chemical balance weighing design is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The incidence matrix of ternary balanced block design is used to construct optimum chemical balance weighing design under the restriction on the number in which each object is weighed.
Keywords: chemical balance weighing design, ternary balanced block design 
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Ceranka, Bronisław; Graczyk, Małgorzata. Optimum chemical balance weighing designs under the restriction on weighings. Discussiones Mathematicae. Probability and Statistics, Tome 21 (2001) no. 2, pp. 111-120. http://geodesic.mathdoc.fr/item/DMPS_2001_21_2_a3/

[1] K.S. Banerjee, Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics, Marcel Dekker Inc., New York 1975.

[2] E.J. Billington, Balanced n-array designs: a combinatorial survey and some new results, Ars Combinatoria 17 A (1984), 37-72.

[3] E.J. Billington and P.J. Robinson, A list of balanced ternary designs with r ≤ 15, and some necessary existence conditions, Ars Combinatoria 16 (1983), 235-258.

[4] B. Ceranka and K. Katulska, Chemical balance weighing designs under the restriction on the number of objects placed on the pans, Tatra Mt. Math. Publ., 17 (1999), 141-148.

[5] B. Ceranka, K. Katulska and D. Mizera, The application of ternary balanced block designs to chemical balance weighing designs, Discuss. Math. Algebra and Stochastic Methods 18 (1998), 179-185.

[6] H. Hotelling, Some improvements in weighing and other experimental techniques, Ann. Math. Stat., 15 (1944), 297-305.

[7] D. Raghavarao, Constructions and Combinatorial Problems in Designs of Experiments, John Wiley Inc., New York 1971.

[8] C.R. Rao, Linear Statistical Inference and its Applications, Second Edition, John Wiley Inc., New York 1973.

[9] M.N. Swamy, Use of balanced bipartite weighing designs as chemical balance designs, Comm. Statist. Theory Methods 11 (1982), 769-785.