Testing of Body Armor Materials Phase III (2012) / Chapter Skim
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Appendix G Determining the Necessary Level of Precision for Body Armor Testing
Appendix G Determining the Necessary Level of Precision for Body Armor Testing
Pages 280-298
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From page 280... ...
Under these conditions, if we assume that the variability of the armor, measured in terms of standard deviations, is 1 mm, then body armor designs with -280
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From page 281... ...
If the backing material exhibits a variance characterized by a standard deviation bck matl , then the true population of BFDs will be x pop 2 1 exp f length ' x ' 2 pop pop 2 2 (G.1) where pop is the mean BFD for that particular armor system (which depends on the mechanical response of the armor and the elastic recovery in the backing material)
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From page 282... ...
The normal distribution given in Figure G-1 is convoluted with a Gaussian spreading function to represent measurement error. The result is another normal distribution with a larger standard deviation, given by the dotted line.
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It decreases the availability of armor directly due to its rejection; concomitantly it increases cost and produces a degree of randomness in the testing that can diminish vendor confidence, because indistinguishable lots of armor will sometimes pass and sometimes fail. The relative contribution of variance in the clay and finite precision in the measurement technique is therefore important and can be assessed quantitatively.
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From page 284... ...
the mean remains the same and the standard deviations are added in quadrature: z 2 1 exp f apparent length ' z ' ( z ) pop 2 pop i2 s pop ins 2 2 2 2 n This is equivalent to the result obtained when there are independent sources of error.
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From page 285... ...
If the standard deviation of the population (in our case determined by RP #1) is held constant, larger values for this ratio indicate progressively more precise measurement techniques.
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From page 286... ...
One important conclusion from this diagram is that replacing the existing backing material, RP #1, with a material having a significantly lower variance, say 1 mm, would require a corresponding increase in the measurement technique, down to 0.1 mm, to keep the relative impact of measurement error constant. Specifically, if we assume pop 3 mm, all BFD measuring devices with standard deviations of less than 0.3 mm are equivalently precise from a practical perspective in terms of yielding useful data for decision making.
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From page 287... ...
ESTIMATION OF THE RELATIVE PRECISION OF MEASUREMENT TECHNIQUES With the aggregate set of data provided to the committee, it is possible to make a quantitative assessment for the techniques employed in cavity measurement in RP #1 on the range. First, the data provided in Figure 4-7a in Chapter 4 indicate the standard deviation of drop test results is between 2 and 3 mm depending on the particular clay box.
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From page 288... ...
? Because both the sample mean and sample standard deviation are stochastic, rather than derive an analytical expression to calculate the probability a manufacturer passes or fails, we simulate it.
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The 90 percent upper tolerance limit must be less than 44 mm with a 90 percent confidence to pass FAT. The solid curve represents how shifting the mean of the armor performance affects the probability of armor being rejected when the standard deviation associated with the population of BFDs is 3 mm (assumed to be dominated by the behavior of the RP #1, the measurement method adding no significant breadth to the distribution, as would be expected of the Faro laser scanner)
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. To the extent that , the standard deviation observed in the test, is mainly the result of the testing methodology (e.g., Roma Plastilina #1)
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There are data available to check whether or not the order-of-magnitude effect expected by this analysis is consistent. The presentation by Ceradyne gives the average BFD and standard deviations for data sets from ESAPI and XSAPI plates -291
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and H.P. White Laboratory with both caliper and laser scanner.71 First, the standard deviations are between 2.93 and 3.82 mm.
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PREPUBLICATION DRAFT -- SUBJECT TO EDITORIAL CORRECTION FIGURE G-6 Photograph, laser scan, and cross section of cavity in RP #1 produced by armor testing that illustrates typical roughness that characterizes the surface of the depression.
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. FIGURE G-7 Digital calipers used in armor testing.
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This roughness of the scanner data is a function of the smoothing algorithm employed. FIGURE G-8 Two images of typical BFD cavities in RP #1 produced by the Faro laser scanner.
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Consider, for example, a manufacturer that passes the first article test and whose armor population has a mean BFD performance of 40 mm with a standard deviation of 3 mm. Then the probability that any individual plate produced by this manufacturer will have a BFD greater than 50 mm is 0.000429.
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FIGURE G-9 The probability a manufacturer will pass the first article, first shot BFD test (solid line) for various population mean BFD levels ()
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2008. Summary Report of Laser Scanning Method Certification Study for Body Armor Backface Deformation Measurements.
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