Chemical balance weighing designs with correlated errors based on balanced block designs

摘要

The paper is studying the estimation problem of individual measurements (weights) of objects using the chemical balance weighing design under the restriction on the number of times in which each object is weighed. We assume that the errors are correlated and they have equal variances. We give the lower bound of variance of each of the estimators and the sufficient and necessary conditions under which this lower bound is attained. The new construction method for the optimum chemical balance weighing design is given. We use the incidence matrices of the balanced incomplete block designs and the ternary balanced block designs to construct the design matrix of the optimum chemical balance weighing designs.