Abstract
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 p 1 + p 2 = q ⩽ p , where p 1 and p 2 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 - 1 X ) - 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.
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