REGULAR D-OPTIMAL SPRING BALANCE WEIGHING DESIGNS: CONSTRUCTION

Abstract

Spring balance weighing design there is the model of experiment in that the result of experiment we can present as linear combination of unknown measurements of objects with factors of this combination equal to zero or one. In the paper we consider such designs under the basic assumption that the errors of measurements are uncorrelated and they have different variances, that means the measurements are taken in different conditions or by used different measurement equipment. We consider D-optimal designs , i.e. the designs in that the determinant of the information matrix for the design attains the maximal value. We give the bounds of its value according to the number of objects in experiment, is it odd or even. The theoretical considerations we illustrate with example of construction of respectively design.