A New Weighing Design1

Some observations on repeated spring balance weighing designs

“…It has been shown here that, while the above findings may be true in some situations, one might, in a given problem, prefer "repeated designs" to those suggested in [3] and [5]. …”

“…Such a design will be called Design IV. Kulshreshtha and Dey [5] have shown that for such a design, the variance factors for the first set of (v-k) estimated weights are less than those given by Design I and Design III. It will be shown here that such variance factors, that is, variance factors under Design IV even for the first set of (v-k) estimated weights are not less than those given by Design II in case of all symmetrical BIBD's.…”

“…Such a BIBD (which we shall call a deleted BIBD) is characterized by the parameters v'=v-k, U=b-1, ~=r, /d=k-2, 2'=2. Kulshreshtha and Dey [5] have suggested an alternative design which is obtained by augmenting the original symmetrical BIBD with the deleted BIBD in a scheme as shown below, giving the new design matrix X in the form, (lo)…”

“…If a BIBD complementary to the above BIBD is used as a weighing design, the value of the corresponding I X'XI will be equal to ( 5 ) (r-…”

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SummaryDey [3] has suggested a spring balance weighing design in preference to "repeated designs ", and later, Kulshreshtha and Dey [5] have suggested yet one more weighing design which, they say, would be preferred to "repeated designs" and to those suggested in [3], provided one is interested in estimating the weights of some of the objects with increased precision at the cost of precision for others. It has been shown here that, while the above findings may be true in some situations, one might, in a given problem, prefer "repeated designs" to those suggested in [3] and [5].

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