Another look at counting by weighing

Abstract

In many instances a fixed number of items, N, must be obtained from a large collection of these items. The process of counting out these items, however, becomes impractical if N is quite large. An alternative to individually counting out N items is counting by weighing. If the mean weight of an individual item, μ, is known, then we simply assemble a batch that weighs Nμ. If the mean weight is unknown, then we take an initial sample of size n, much less than N, from which an estimate, m, of the mean weight is obtained. We then assemble a batch that weighs (N−n)m.This procedure leads in principle to a set of N total items (n counted, N−n weighed). By way of renewal theory, this article examines the distributional properties of the actual number of items in the batch. Further, from the distributional properties of the actual number of items counted, this, article addresses the problem of determining the smallest initial sample size n for estimating N to within some specified bound with high probability. Also, refinements known as overshoot and continuityw corrections are implemented to improve the procedure. Finally, a simulation study was performed to evaluate the performance of the procedure.

Keywords:

• coefficient of variation
• renewal theory
• overshoot correction
• sequential sampling rule