New Results Regarding the Construction Method for D‑optimal Chemical Balance Weighing Designs

Bronisław Ceranka; Małgorzata Graczyk

doi:10.18778/0208-6018.349.08

Authors

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

DOI:

https://doi.org/10.18778/0208-6018.349.08

Keywords:

balanced bipartite weighing design, balanced incomplete block design, chemical balance weighing design, D‑optimality, ternary balanced block design

Abstract

We study an experiment in which we determine unknown measurements of p objects in n weighing operations according to the model of the chemical balance weighing design. We determine a design which is D‑optimal. For the construction of the D‑optimal design, we use the incidence matrices of balance incomplete block designs, balanced bipartite weighing designs and ternary balanced block designs. We give some optimality conditions determining the relationships between the parameters of a D‑optimal design and we present a series of parameters of such designs. Based on these parameters, we will be able to set down D‑optimal designs in classes in which it was impossible so far.

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