Open AccessNotes on D‑optimal Spring Balance Weighing Designs
Author(s) -
Bronisław Ceranka,
Małgorzata Graczyk
Publication year - 2018
Publication title -
acta universitatis lodziensis. folia oeconomica
Language(s) - English
Resource type - Journals
eISSN - 2353-7663
pISSN - 0208-6018
DOI - 10.18778/0208-6018.338.11
Subject(s) - upper and lower bounds , mathematics , balance (ability) , value (mathematics) , spring (device) , optimal design , statistics , matrix (chemical analysis) , mathematical optimization , algorithm , mathematical analysis , engineering , structural engineering , medicine , physical medicine and rehabilitation , materials science , composite material
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.