TITLE:
A Two-Parameter Description for the Injury Risk of Flash Bangs with Uncertainty
AUTHORS:
Hongyun Wang, Matthew Simms, George Labaria, Wesley A. Burgei, Hong Zhou
KEYWORDS:
Flash Bangs, Actual Number of Injured in a Crowd, Fluctuations in the Hidden Injury Probability, Simplified Phenomenological Models
JOURNAL NAME:
American Journal of Operations Research,
Vol.9 No.3,
May
16,
2019
ABSTRACT: We study the random injury outcome caused by multiple flash bang submunitions
on a crowd. We are particularly interested in the fluctuations in injury
outcome among individual realizations. Previously, to simulate the distribution
of the actual number of injured, we developed a comprehensive Monte
Carlo model. While the full computational model is important for thorough
theoretical investigations, in practical operations, it is desirable to characterize
the phenomenological behavior of injury outcome using a concise model
with only one or two parameters. Conventionally, the injury outcome is indicated
by the average fraction of injured, which is called the risk of significant
injury (RSI). The single metric RSI description fails to capture fluctuations in
the injury outcome. The number of injured in the crowd is influenced by
many random factors: the aiming error of flash bang mortar, the dispersion
of submunitions after mortar burst, the amount of acoustic dose reaching individual
subjects, and the biovariability of individual subjects’ reactions to a
given acoustic dose. We aim to include these random factors properly and
concisely. In this study, we represent the random injury outcome as a compound
binomial model, in which the hidden injury probability is drawn from
a two-parameter model distribution. We formulate and examine six model
distributions for the injury probability. The best performer is a mixture of
uniform and triangle distributions, parameterized by (RSI, dp) where dp is
the standard deviation of the hidden injury probability. This mixture model
predicts the behavior of injury outcome with uncertainty, based solely on the
two parameters (RSI, dp) in the flash bang description. For example, we can
predict the probability of the injury outcome not exceeding a prescribed tolerance.
We advocate the adoption of this two-parameter characterization for
flash bangs to replace the single-parameter RSI description. Whenever we
need to give a high level coarse description of a flash bang situation, we state that the injury risk is represented by (RSI, dp).