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Optimum singular spring balance weighing designs with non-homogeneity of the variances of errors for estimating the total weight. (English) Zbl 0657.62082
The problem of estimation of the total weight of objects using a singular spring balance weighing design with non-homogeneity of the variances of errors has been dealt with. Based on a theorem giving a lower bound for the variance of the estimated total weight, a necessary and sufficient condition for this lower bound to be attained is obtained. It is shown that weighing designs for which the lower bound is attainable, can be constructed from the incidence matrices of $$(\alpha_ 1$$,..., $$\alpha_ t)$$-resolvable block designs, $$\alpha$$-resolvable block designs, singular group divisible designs, and semi-regular group divisible designs.

MSC:
 62K05 Optimal statistical designs
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