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When it is necessary to manually count a large number N s of items, significant time and energy can be saved by weighing the items. When the weights are random with unknown mean and variance, one procedure is to take a small sample of n items, weigh them, and add more items until the total weight reaches N s times the average weight of the n items. This procedure yields a batch of items. An estimation criterion used in Yu (1989) yields an optimal value n * for the original sample, but it is not useful when the coefficient of variation is unknown. To overcome this, Yu (1989) proposed a fully, sequential scheme. Here, we propose a relatively new sequential sampling scheme due to Liu (1997a). Our scheme and Yu's (1989) scheme are shown to be second-order efficient, but our scheme requires substantially fewer sampling operations. These show that a little bit of sampling using substantially fewer sampling operations can significantly reduce the effort and cost of complete counting. [ABSTRACT FROM AUTHOR]

Considerable time and energy involved in complete counting of large, but pre-specified, batch of Ns items could be saved by using weights of items. This article considers the case when the underlying distribution of weights, and its mean and variance are unknown. The problem is then reduced to that of finding an estimator of the mean and an optimal (small) sample size based on which a number [Ncirc]n of items in the batch can be determined. Using a fixed-width interval criterion, Nickerson [Nickerson, D.M. Another look at counting by weighing. Commun. Statist. Simula. 1993, 22 (2), 323–343] derived an optimal sample size, but it depends on the unknown coefficient of variation. For this case, we propose a batch-type sequential sampling scheme which requires substantially fewer sampling operations and no prior knowledge of the coefficient of variation, but performs as well as Nickerson's and other available procedures in the literature. This shows that a little bit of sampling using substantially fewer sampling operations can significantly reduce the effort of complete counting. [ABSTRACT FROM AUTHOR]