James Yen, Keith Eberhardt
The U.S. Justice Department's National Institute of Justice (NIJ) has issued several voluntary standards for body armor. NIST's Office of Law Enforcement Standards, with the help of SED statisticians, has been involved in the formulation and analysis of testing related to the standards.
Since most testing of body armor is destructive, the protective vests tested are supposed to be samples representative of their make and model. In the past, goats wore samples of body armor or their constituent material and were subjected to controlled live fire. The extent of the ensuing damage to the armor and the goats indicated the vulnerability of the armor. Nowadays, testing involves firing rounds at vests placed on blocks of modelling clay or a similar material.
The current testing protocol prescribes a full factorial design, where the factors include: 2 types of bullet for each model of vest, whether the vest is dry or wet during testing, the front or back of the vest, and six predetermined locations on each side of the vest tested. Thus, each test of a model of body armor includes 4 vests of that model each being shot 12 times for a total of 48 shots per model. The vest model fails the test if any of the 48 shots penetrates. In addition, the vest model may also be failed if a chosen shot leaves a crater in the clay commensurate to a severe injury in a corresponding human.
Many argue that the problem has not been that of police officers being killed by bullets penetrating ineffective body armor; instead, it has been that of officers being fatally shot when not wearing body armor. If manufacturers make vests heavier and stiffer in order to pass extremely stringent tests, then the increased bulk and cost of these vests may make them less likely to be worn by officers and less likely to bought by police departments.
Because of these concerns, there have been questions about how many shots should comprise a suitable test. If each shot has a fixed positive probability p of penetrating the vest, then the probability of the vest failing the test rises with the number of shots in the test. The figure diagrams the differing probabilities of a vest model passing tests with 24 and 48 shots respectively, under the simplifying assumption that each shot has a fixed probability p of penetration; while the two curves are often close, there is a considerable difference in the failure rates when p is around 0.03.
Ongoing analysis is addressing additional questions about body armor testing. For example, what are the differences between shots that hit the vest straight on and those that hit at an angle? Also, how does wet armor perform compared to dry armor?
Figure 8: This figure graphs the probabilities of a vest model passing tests with 24 and 48 shots respectively, as a function of the penetration probility p, where we have made the simplifying assumption that each shot has a fixed probability p of penetration. That assumption implies that that the probability of passing the test is (1-p)N, where N is the number of shots in the test. The difference in the respective passing rates is largest at around p= 0.03. Note: The axis for p is logarithmically scaled.
Date created: 7/20/2001