Counting by Weighing: An Alternative Sampling Scheme

Abstract

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.

Keywords:

• Sampling scheme
• Second-order expansion
• Uniformly integrable

Subject Classification:

• 62L12
• 62G99

ACKNOWLEDGMENTS

We thank the two referees for their comments and suggestions, which have improved the presentation of the article. We especially thank one of the referees for a very careful reading of the article and for pointing out some errors and corrections in the earlier version. We also thank one of the referees for broadening our simulation study to include a multistage sampling procedure due to Liu (1997b). Sriram's research was partially supported by NSF grant SES-0241651.

Notes

Recommended by Basil M. de Silva