TWARON – Bullet-proof Math #SWI2006

Twaron is a strong fiber. Teijin Twaron is a split off from AKZO-Nobel, and is now
part of Teijin, a Japanese company. Teijin Twaron is responsible for developing the
Twaron fiber and its applications.
One of the applications of Twaron is in bullet-proof vests. Twaron is interested in
finding the velocity at which only a small proportion (say 1 promille) of the bullets
passes through the vests. This speed is denoted V01. Also required is at which speed
half of the bullets pass through the vest, which is denoted by V50.
For the V01 no method is yet defined, for the V50 a NATO standard method of
testing exists. It is now generally accepted by yarn manufacturers, vest producers and
end-users that this NATO standard test can lead to inaccurate test-results.
With the current V50 method, on the basis of experimental experience (which is
irrelevant for us at this point), we guess what V50 should be. Then, on the basis of
this estimate, we perform a test as follows:
We shoot a bullet at the expected V50 speed. Depending on whether it passes through
or not, we shoot bullets a little slower or faster until 3 stops and 3 perforations are
registered. The estimate for V50 is the average of these speeds. ,
This method can lead to different results for identical bullet proof vests.
It is observed that the overall distribution curve of shooting data is not covered by the
NATO procedure. This can lead to the different results for the V50 estimate.

Currently a lot of data is present that describes whether bullets pass through the vests
or not, but the problem is to develop a good (statistical) model for this. Using this
model, the result must be the values for V01 and V50 including the confidence
There are a number of approaches taken in the current literature, but there does not
seem to be reasoning behind these approaches. One of these is to fit a Gaussian curve
through the curve of estimated probabilities, and to fit the parameters by a suitable
minimization procedure. This does not give a good fit. The key question is how to do
this better. Partial problems are:
1. What is a good model do describe whether the bullets pass through the vest?
2. If we have such a model, how do we estimate the parameters V01 and V50?


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TWARON – Bullet-proof Math