ceptably small, and (b) to estimate the size of these error rates for a given procedure, which need to be communicated along with the assertions of a match or a non-match so that the reliability of these assertions is understood.1 Our general approach is to outline some of the possibilities and recommend specific statistical approaches for assessing matches and non-matches, leaving to others the selection of one or more critical values to separate cases 1), 2), and perhaps 3) above.2

Given the data on any two bullets (e.g., CS and PS bullets), one crucial objective of compositional analysis of bullet lead (CABL) is to provide information that bears on the question: “What is the probability that these two bullets were manufactured from the same CIVL?” While one cannot answer this question directly, CABL analysis can provide relevant evidence, the strength of that evidence depending on several factors.

First, as indicated in this chapter, we cannot guarantee uniqueness in the mean concentrations of all seven elements simultaneously. However, there is certainly variability between CIVLs given the characteristics of the manufacturing process and possible changes in the industry over time (e.g., very slight increases in silver concentrations over time). Since uniqueness cannot be assured, at best, we can address only the following modified question:

“What is the probability that the CS and PS bullets would match given that they came from the same CIVL compared with the probability that they would match if they came from different CIVLs?”

The answer to this question depends on:

1. the number of bullets that can be manufactured from a CIVL,

2. the number of CIVLs that are analytically indistinguishable from a given CIVL (in particular, the CIVL from which the CS bullet was manufactured), and

3. the number of CIVLs that are not analytically indistinguishable from a given CIVL.

The answers to these three items will depend upon the type of bullet, the manufacturer, and perhaps the locale (i.e., more CIVLs may be more readily accessible to residents of a large metropolitan area than to those in a small urban town). A carefully designed sampling scheme may provide information from

1  

This chapter is concerned with the problem of assessing the match status of two bullets. If, on the other hand, a single CS bullet were compared with K PS bullets, the usual issues involving multiple comparisons arise. A simple method for using the results provided here to assess false match and false non-match probabilities is through use of Bonferroni’s inequality. Using this method, if the PS bullets came from the same CIVL, an estimate of the probability that the CS bullet would match at least one of the PS bullets is bounded above by, but often very close to, K times the probability that the CS bullet would match a single PS bullet.

2  

The purposive selection of disparate bullets by those engaged in crimes could reduce the value of this technology for forensic use.



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