A Highly D‑efficient Spring Balance Weighing Design for an Even Number of Objects

Małgorzata Graczyk; Bronisław Ceranka

doi:10.18778/0208-6018.344.02

Authors

Małgorzata Graczyk Poznań University of Life Sciences, Faculty of Agronomy and Bioengineering Department of Mathematical and Statistical Methods https://orcid.org/0000-0002-5550-7007
Bronisław Ceranka Poznań University of Life Sciences, Faculty of Agronomy and Bioengineering Department of Mathematical and Statistical Methods https://orcid.org/0000-0002-5395-1593

DOI:

https://doi.org/10.18778/0208-6018.344.02

Keywords:

highly D-efficient design, spring balance weighing design

Abstract

The problem of determining unknown measurements of objects in the model of spring balance weighing designs is presented. These designs are considered under the assumption that experimental errors are uncorrelated and that they have the same variances. The relations between the parameters of weighing designs are deliberated from the point of view of optimality criteria. In the paper, designs in which the product of the variances of estimators is possibly the smallest one, i.e. D‑optimal designs, are studied. A highly D‑efficient design in classes in which a D‑optimal design does not exist are determined. The necessary and sufficient conditions under which a highly efficient design exists and methods of its construction, along with relevant examples, are introduced.

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