A-optimal chemical balance weighing design with nonhomogeneity of variances of errors

The problem studied in the paper concerns the estimation of individual weights of p objects according to the model of an A-optimal chemical balance weighing design with a positive definite diagonal variance matrix of errors under the restriction p1+p2=q[less-than-or-equals, slant]p, where p1 and p2 represent the numbers of objects placed on the left and on the right pan, respectively, in each of the measurement operations. The lower bound of tr(X'G-1X)-1 is obtained and the necessary and sufficient condition for this lower bound to be attained is given. To construct the A-optimal chemical balance weighing design the incidence matrices of the balanced bipartite weighing designs are used.