Methods for analyzing the uncertainty of a reconstructed result in a traffic accident with interval and probabilistic traces

•A probabilistic-interval method was proposed.•An algorithm was proposed to shorten the time taken for finding out the upper and lower bound.•An improved probabilistic-interval method was proposed.•The time taken for the improved method was far less than the Monte Carlo method's.•Numerical and true accident are given to validate the feasibility of these methods.

In order to make the reconstructed result more reliable, a method named improved probabilistic-interval method was proposed to analyze the uncertainty of a reconstructed result in a traffic accident with probabilistic and interval traces. In the method, probabilistic traces are replaced by probabilistic sub-intervals firstly; secondly, these probabilistic sub-intervals and those interval traces will be combined to form many new uncertainty analysis problems with only interval traces; thirdly, the upper and lower bound of the reconstructed result and their probability were calculated in each new uncertainty analysis problem, and an algorithm was proposed to shorten the time taken for this step; finally, distribution functions of the upper and lower bound of the reconstructed result were obtained by doing statistic analysis. Through 2 numerical cases, results obtained from the proposed method were almost the same as results obtained from the Monte Carlo method, but the time taken for the proposed method was far less than the time taken for the Monte Carlo method and results obtained from the proposed method were more stable. Through applying the proposed method to a true vehicle-pedestrian accident, not only the upper and lower bound of the impact velocity (v) can be obtained; but also the probability that the upper bound and the lower bound of v falls in an arbitrary interval can be obtained; furthermore, the probability that the interval of v is less than an arbitrary interval can be obtained also. It is concluded that the proposed improved probabilistic-interval method is practical.