Optimum chemical balance weighing design with diagonal matrix of errors based on balanced block designs

Abstract

The paper is studying the estimation problem of individual weights of objects using the chemical balance weighing design under the restriction on the number of times in which each object is weighed. Additionally, we assume that the errors are uncorrelated and they have different variances. There are given the lower bound of the variance of each of the estimated weights and the sufficient and necessary conditions under which this lower bound is attained. For the new construction method for optimum chemical balance weighing designs, we use the incidence matrices of the balanced incomplete block designs and the balanced bipartite weighing designs.