Ball, J., Danaher, D., and Ziernicki, R., "Considerations for Applying and Interpreting Monte Carlo Simulation Analyses in Accident Reconstruction," SAE Technical Paper 2007-01-0741, 2007, doi:10.4271/2007-01-0741.
In reconstructing any accident, the reconstructionist must properly account for uncertainty in their analysis. One popular method of examining and quantifying the uncertainty within an analysis is the use of Monte Carlo simulation techniques. The methods have been well established and published over the last several years by numerous authors. One of the key factors underlying the Monte Carlo analysis is the assumed probability distribution of the individual factors within the analysis. The literature has examples and recommendations for assuming normal, uniform, or custom distributions for input parameters. However, the literature to date has not examined how the assumption of a distribution affects the resulting probability distribution of the Monte Carlo analysis. This paper attempts to address this issue. Furthermore, with the large number of samples typically considered during a Monte Carlo analysis, the resulting probability distribution tends to be normal and lends itself well to statistical interpretation as to the “most likely” range of the desired parameter. The analysis in this paper was performed with a plug-in to Excel called Crystal Ball®, and the version of Crystal Ball® used for this paper allows the user to selectively filter results which do not agree with physical reality (for example, non-equal force balances within a crush energy analysis). When filtering results, the final probability distribution can be skewed. This paper also examines methods of identifying the “most likely” range from within a skewed probability distribution.