Open AccessON D-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGNS
Author(s) -
Bronisław Ceranka,
Małgorzata Graczyk
Publication year - 2015
Publication title -
acta universitatis lodziensis. folia oeconomica
Language(s) - English
Resource type - Journals
eISSN - 2353-7663
pISSN - 0208-6018
DOI - 10.18778/0208-6018.311.08
Subject(s) - block (permutation group theory) , balance (ability) , ternary operation , mathematics , optimal design , incidence matrix , mathematical optimization , block design , computer science , statistics , combinatorics , engineering , medicine , structural engineering , node (physics) , physical medicine and rehabilitation , programming language
The paper deals with the problem of determining the chemical balance weighing designs satisfying the criterion of D-optimality under assumption that the measurement errors are equal correlated and they have the same variances. The existence conditions and the form of the optimal design are given. Moreover, some construction methods of the design matrices based on the incidence matrices of the balanced incomplete block designs and ternary balanced block designs are presented. Any example of construction is given.