Monte Carlo Techniques for Correlated Variables in Crash Reconstruction

The results of a traffic crash reconstruction often include vehicle speeds to address causation and changes in velocity to indicate crash severity. Since these results are related, they should be modeled in a probabilistic context as a joint distribution. Current techniques in the traffic crash reconstruction literature assume the the input parameters and results of an analysis are independent, which may or may not be appropriate. Therefore, a discussion of uncertainty propagation techniques with correlation and Monte Carlo simulation of correlated variables is presented in this paper. The idea that measuring a parameter with a common instrument induces correlation is explored by examining the process of determining vehicle weights. Also, an example of determining the energy from crush is presented since the A and B stiffness coefficients are correlated. Results show the difference between accounting for correlation and assuming independence may be significant. However, the examples provided are aimed at introducing the concept of correlation in Monte Carlo simulation and determining the practical significance of correlation have yet to be determined. Furthermore, interpreting and presenting results from simple Monte Carlo analysis of a momentum problem requires using the concepts of joint, marginal, and conditional distributions to fully understand the results.