Interval Estimation Approach to Counting by Weighing: A Sequential Scheme

Abstract

Considerable time and energy involved in complete counting of large, but pre-specified, batch of N _s 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.

Key Words:

• Coefficient of variation
• Fixed-width interval
• Continuity correction
• Batch-type sequential sampling

AMS 2000 Subject Classifications:

• Primary 62L12
• Secondary 62G99

Acknowledgments

We would like to thank the two referees for suggesting some additions, changes and references which have led to a substantial improvement in the presentation. T.N. Sriram's research was partially supported by NSF grant SES-0241651.