Some Practical Techniques in Serial Number Analysis

The problem discussed is that of sampling from continuous and discrete uniform distributions. An application of this problem is presented which deals with the analysis of serial numbers on manufactured items in order to estimate the total number of items manufactured. Estimates of bounded relative error are obtained. Some justification for the use of these estimates is presented from the loss (cost) function point of view. Confidence intervals for the parameters are obtained and graphs are presented which may be used to determine the sample size required for confidence intervals of a given expected relative length. Tests of hypotheses are discussed. A method is presented for determining whether the serial numbers obtained are a random sample from a population of consecutive serial numbers. 1 1 The author is indebted to Mr. William A. Aronow, New Holland Machine Company, and to Professor Harry V. Roberts, University of Chicgo, for very helpful comments.