Reliability Analysis of the Empirical Bayes Method in Estimating Crash Frequency on Two-Lane, Two-Way Rural Highways

Road traffic crashes are a leading cause of death across all age groups, particularly among children and young adults. This study evaluates the reliability of the empirical Bayes (EB) method for predicting crash frequencies to improve road safety decision-making. The EB method, initially introduced in an earlier road safety study, has been widely adopted and promoted by the Highway Safety Manual (HSM) as a standard approach for estimating crash frequencies. Despite the application of the EB method and the calibration procedures recommended by the HSM, uncertainties may still arise because of the inclusion of diverse crash-related variables in the prediction model. Reliability analysis, employing limit state functions and the Monte Carlo sampling method, was used to assess the probability of noncompliance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>nc</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> between expected and observed crash frequencies, and to identify and rank the sources of uncertainty in the model. The case study included 64 segments of two-lane, two-way rural highways in Iran, with 34 tangents and 30 horizontal curves. Based on actual geometric and traffic data, all EB model variables were computed. The results revealed segment-specific <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>nc</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and a ranking of model variables was established using importance vectors to identify the most influential sources of uncertainty.