Optimum chemical balance weighing designs under the restriction on weighings

• Autorzy: Bronisław Ceranka , Małgorzata Graczyk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

chemical balance weighing design; ternary balanced block design

Kategorie tematyczne

• 62K15: Factorial designs

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 111-120

Daty

wydano

2001

otrzymano

2001-12-12

Twórcy

autor

Bronisław Ceranka

• Department of Mathematical and Statistical Methods, Agricultural University of Poznań, Wojska Polskiego 28, 60-637 Poznań, Poland

autor

Małgorzata Graczyk

• Department of Mathematical and Statistical Methods, Agricultural University of Poznań, Wojska Polskiego 28, 60-637 Poznań, Poland

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmps.1024