ON D-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGNS

Bronisław Ceranka; Małgorzata Graczyk

doi:10.18778/0208-6018.311.08

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/10.18778/0208-6018.311.08

Keywords:

balanced incomplete block design, chemical balance weighing design, D-optimality, ternary balanced block design

Abstract

The paper deals with the problem of determining the chemical balance weighing designs satisfying the criterion of D-optimality under assumption that the measurement errors are equal correlated and they have the same variances. The existence conditions and the form of the optimal design are given. Moreover, some construction methods of the design matrices based on the incidence matrices of the balanced incomplete block designs and ternary balanced block designs are presented. Any example of construction is given.

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References

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

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

Ceranka B., Graczyk M. (2010), Notes about singular chemical balance weighing design. Acta Universitatis Lodziensis, Folia Oeconomica 235, 241 – 246.

Ceranka B., Graczyk M. (2012), Notes on the optimum chemical balance weighing design, Acta Universitatis Lodziensis, Folia Oeconomica, 269, 91-101.

Ceranka B., Graczyk M. (2014), On certain A-optimal biased spring balance weighing designs, Statistics in Transition new series, 15, 317-326.

Gail Z., Kiefer J. (1982), Construction methods for D-optimum weighing designs when , Annals of Statistics, 10, 502-510.

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

Jacroux M., Notz W. (1983), On the optimality of spring balance weighing designs, The Annals of Statistics, 11, 970-978.

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.

Katulska K., Smaga Ł. (2010), On some construction of D-optimal chemical balance weighing designs, Colloquium Biometricum, 40, 155-164.

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

Koukouvinos Ch. (1996), Linear models and D-optimal designs, Statistics

and Probability Letters, 26, 329-332.

Koukouvinos Ch., Seberry J. (1997), Weighing matrices and their applications, Journal of Statistical Planning and Inference, 62, 91-101.

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

Raghavarao D. (1971), Constructions and Combinatorial Problems in Design of Experiment, John Wiley and Sons. New York

Raghavarao D., Padgett L.V. (2005), Block Designs, Analysis, Combinatorics and Applications, Series of Applied Mathematics 17, Word Scientific Publishing Co. Pte. Ltd., Singapore.

Rao C.R. (1973), Linear Statistical Inference and its Applications, John Wiley and Sons Inc., New York.

Shah K.R., Sinha B.K. (1989), Theory of Optimal Designs, Springer-Verlag, Berlin.