A Two-Parameter Description for the Injury Risk of Flash Bangs with Uncertainty

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).