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Keywords:
chemical balance weighing design; ternary balanced block design
chemical balance weighing design; ternary balanced block design
Summary:
The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for $p = v$ objects implies the existence of an optimum chemical balance weighing design for $p = v + 1$ objects are given. The existence of an optimum chemical balance weighing design for $p = v + 1$ objects implies the existence of an optimum chemical balance weighing design for each $p < v + 1$. The new construction method for optimum chemical balance weighing design for $p = v + 1$ objects is given. It uses the incidence matrices of ternary balanced block designs for v treatments.
References:
[1] Banerjee K. S.: Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics. Marcel Dekker, New York 1975 MR 0458751 | Zbl 0334.62030
[2] Billington E. J.: Balanced $n$-array designs: a combinatorial survey and some new results. Ars Combin. 17A (1984), 37–72 MR 0746174
[3] Billington E. J., Robinson P. J.: A list of balanced ternary block designs with $r \le 15$ and some necessary existence conditions. Ars Combin. 16 (1983), 235–258 MR 0734059
[4] Ceranka B., Graczyk M.: Optimum chemical balance weighing designs under the restriction on weighings. Discuss. Math. 21 (2001), 111–120 DOI 10.7151/dmps.1024 | MR 1961022
[5] Ceranka B., Katulska K.: On some optimum chemical balance weighing designs for $v+1$ objects. J. Japan Statist. Soc. 18 (1988), 47–50 MR 0959679 | Zbl 0651.62072
[6] Ceranka B., Katulska K.: Chemical balance weighing designs under the restriction on the number of objects placed on the pans. Tatra Mt. Math. Publ. 17 (1999), 141–148 MR 1737701 | Zbl 0988.62047
[7] Ceranka B., Katulska, K., Mizera D.: The application of ternary balanced block designs to chemical balance weighing designs. Discuss. Math. 18 (1998), 179–185 MR 1687875
[8] Hotelling H.: Some improvements in weighing and other experimental techniques. Ann. Math. Statist. 15 (1944), 297–305 DOI 10.1214/aoms/1177731236 | MR 0010951 | Zbl 0063.02076
[9] Raghavarao D.: Constructions and Combinatorial Problems in Designs of Experiments. Wiley, New York 1971 MR 0365935
[10] Saha G. M., Kageyama S.: Balanced arrays and weighing designs. Austral. J. Statist. 26 (1984), 119–124 DOI 10.1111/j.1467-842X.1984.tb01225.x | MR 0766612 | Zbl 0599.62089
[11] Shah K. R., Sinha B. L.: Theory of Optimal Designs. Springer, Berlin 1989 MR 1016151 | Zbl 0688.62043
[12] Swamy M. N.: Use of balanced bipartite weighing designs as chemical balance designs. Comm. Statist. Theory Methods 11 (1982), 769–785 DOI 10.1080/03610928208828270 | MR 0651611 | Zbl 0514.62086
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