Highly D‑efficient Weighing Design and Its Construction

Bronisław Ceranka; Małgorzata Graczyk

doi:10.18778/0208-6018.331.09

Authors

Bronisław Ceranka Poznań University of Life Sciences, Faculty of Agronomy and Bioengineering, Department of Mathematical and Statistical Methods
Małgorzata Graczyk Uniwersytet Przyrodniczy w Poznaniu, Wydział Rolnictwa i Bioinżynierii, Katedra Metod Matematycznych i Statystycznych

DOI:

https://doi.org/10.18778/0208-6018.331.09

Keywords:

balanced incomplete block design, efficient design, group divisible design, optimal design, spring balance weighing design

Abstract

In this paper, some aspects of design optimality on the basis of spring balance weighing designs are considered. The properties of D‑optimal and D‑efficiency designs are studied. The necessary and sufficient conditions determining the mentioned designs and some new construction methods are introduced. The methods of determining designs that have the required properties are based on a set of incidence matrices of balanced incomplete block designs and group divisible designs.

Downloads

Download data is not yet available.

References

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

Bulutoglu D.A., Ryan K.J. (2009), D‑optimal and near D‑optimal 2k fractional factorial designs of resolution V, “Journal of Statistical Planning and Inference”, vol. 139, pp. 16–22.
Google Scholar

Ceranka B., Graczyk M. (2014a), The problem of D‑optimality in some experimental designs, “International Journal of Mathematics and Computer Application Research”, vol. 4, pp. 11–18.
Google Scholar

Ceranka B., Graczyk M. (2014b), Regular E‑optimal spring balance weighing designs with correlated errors, “Communication in Statistics – Theory and Methods”, vol. 43, pp. 947–953.
Google Scholar

Ceranka B., Graczyk M. (2014c), On certain A‑optimal biased spring balance weighing designs, “Statistics in Transition new series”, vol. 15(2), pp. 317–326.
Google Scholar

Ceranka B., Graczyk M. (2016), Recent developments in D‑optimal spring balance weighing designs, to appear.
Google Scholar

Ceranka B., Graczyk M. (2017), Highly D‑efficient designs for even number of objects, Revstat.
Google Scholar

Clatworthy W.H. (1973), Tables of Two‑Associated‑Class Partially Balanced Design, NBS Applied Mathematics Series 63.
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”, vol. 8, pp. 213–240.
Google Scholar

Masaro J., Wong C.S. (2008a), Robustness of A‑optimal designs, “Linear Algebra and its Applications”, vol. 429, pp. 1392–1408.
Google Scholar

Masaro J., Wong C.S. (2008b), D‑optimal designs for correlated random errors, “Journal of Statistical Planning and Inference”, vol. 130, pp. 4093–4106.
Google Scholar

Neubauer M.G., Watkins S., Zeitlin J. (1997), Maximal j‑simpplices in the real d‑dimensional unit cube, “Journal of Combinatorial Theory”, Ser. A 80, pp. 1–12.
Google Scholar

Raghavarao D. (1971), Constructions and combinatorial problems in design of experiment, John Wiley and Sons, New York.
Google Scholar

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

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