Notes on D‑optimal Spring Balance Weighing Designs

Bronisław Ceranka; Małgorzata Graczyk

doi:10.18778/0208-6018.338.11

Authors

Bronisław Ceranka Poznań University of Life Sciences, Faculty of Agronomy and Bioengineering, Department of Mathematical and Statistical Methods
Małgorzata Graczyk Poznań University of Life Sciences, Faculty of Agronomy and Bioengineering, Department of Mathematical and Statistical Methods

DOI:

https://doi.org/10.18778/0208-6018.338.11

Keywords:

D-optimal design, spring balance weighing design

Abstract

Spring balance weighing design is a model of an experiment in which the result can be presented as a linear combination of unknown measurements of objects with factors of this combination equalling zero or one. In this paper, we assume that the variances of measurement errors are not equal and errors are not correlated. We consider D‑optimal designs, i.e. designs in which the determinant of the information matrix for the design attains the maximal value. The upper bound of its value is obtained and the conditions for the upper bound to be attained are proved. The value of the upper bound depends on whether the number of objects in the experiment is odd or even. Some methods of construction of regular D‑optimal spring balance weighing designs are demonstrated.

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