CONSTRUCTION METHOD OF A-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGNS

Bronisław Ceranka; Małgorzata Graczyk

doi:10.18778/0208-6018.314.06

Authors

Bronisław Ceranka Department of Mathematical and Statistical Methods Poznań University of Life Sciences
Małgorzata Graczyk Department of Mathematical and Statistical Methods Poznań University of Life Sciences

DOI:

https://doi.org/10.18778/0208-6018.314.06

Keywords:

A-optimality, balanced bipartite weighing design, chemical balance weighing design, ternary balanced block design

Abstract

Here, we study the design in that we determine unknown measurements of p objects by used of n measurement operations. For that reason we consider the chemical balance weighing design under assumption that the measurement errors are uncorrelated and they have the same variances. We give new construction method of the A-optimal chemical balance weighing design based on the incidence matrices of the balanced bipartite weighing designs and the ternary balanced block designs. The consequence of the proposed method is widening of possible classes in that A-optimal design exists.

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References

Banerjee K.S. (1975), Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics, Marcel Dekker Inc., New York.
Google Scholar

Billington E.J. (1984), Balanced n-ary designs: a combinatorial survey and some new results, Ars Combin., 17 A, 133-144.
Google Scholar

Ceranka B., Graczyk M. (2007), A-optimal chemical balance weighing design under certain condition, Metodološki Zvezki–Advances in Methodology and Statistics, 4, 1-7.
Google Scholar

Ceranka B., Graczyk M. (2012), Robustness of optimal chemical balance weighing designs for estimation total weight, Communication in Statistics-Theory and Methods, 41, 2297-2304.
Google Scholar

Ceranka B., Graczyk M. (2014), Construction of the regular D-optimal weighing designs with non-negative correlated errors, Colloquium Biometricum, 44, 43-56.
Google Scholar

Graczyk M. (2013): Some applications on weighing designs, Biometrical Letters, 50, 15-26.
Google Scholar

Jacroux M., Wong C.S., Masaro J.C. (1983), On the optimality of chemical balance weighing design, Journal of Statistical Planning and Inference, 8, 213-240.
Google Scholar

Katulska K., Smaga Ł. (2013), A note on D-optimal chemical balance weighing designs and their applications, Colloquium Biometricum, 43, 37-45.
Google Scholar

Masaro J., Wong C.S. (2008), Robustness of A-optimal designs, Linear Algebra and its Applications, 429, 1392-1408.
Google Scholar

Swamy M.N. (1982), Use of the balanced bipartite weighing designs, Comm. Statist. Theory Methods, 11, 769-785.
Google Scholar