Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors

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

Abstrakty

EN

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.

Słowa kluczowe

EN

balanced bipartite weighing design; chemical balanceweighing 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: 2004
• Tom: 24
• Numer: 2
• Strony: 215-232

Daty

wydano

2004

otrzymano

2004-01-10

poprawiono

2004-08-04

Twórcy

autor

Bronisław Ceranka

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

autor

Małgorzata Graczyk

• Department of Mathematical and Statistical Methods, Agricultural University, 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] B. Ceranka and M. Graczyk, Optimum chemical balance weighing designs under the restriction on weighings, Discussiones Mathematicae - Probability and Statistics 21 (2001), 111-120.
• [3] 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.
• [4] B. Ceranka, K. Katulska and D. Mizera, The application of ternary balanced block designs to chemical balance weighing designs, Discussiones Mathematicae - Algebra and Stochastic Methods 18 (1998), 179-185.
• [5] H. Hotelling, Some improvements in weighing and other experimental techniques, Ann. Math. Stat. 15 (1944), 297-305.
• [6] C. Huang, Balanced bipartite weighing designs, Journal of Combinatorial Theory (A) 21 (1976), 20-34.
• [7] K. Katulska, Optimum chemical balance weighing designs with non - homegeneity of the variances of errors, J. Japan Statist. Soc. 19 (1989), 95-101.
• [8] J.W. Linnik, Metoda Najmniejszych Kwadratów i Teoria Opracowywania Obserwacji, PWN, Warszawa 1962.
• [9] D. Raghavarao, Constructions and Combinatorial Problems in Design ofExperiments, John Wiley Inc., New York 1971.
• [10] C.R. Rao, Linear Statistical Inference and its Applications, Second Edition, John Wiley and Sons, Inc., New York 1973.
• [11] 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.1054