To promote the application of reliability analysis (probabilistic geometric design) in highway safety design and crash prediction

this paper develops crash prediction models to establish the relationship between the multi-mode failure probability of cars and car crashes. Firstly

considering the multi-mode failure as the breakthrough point

a multi-mode failure system was established based on three possible failure modes (skidding

rollover

and insufficient sight distance) of single-car on combination sections of vertical and horizontal curves. Then

10 241 single-car crashes on the combination sections of vertical and horizontal curves of highway in Washington were taken as the research objects

and the multi-mode failure probability of the system was solved by Monte Carlo and wide bound method. Finally

three crash prediction models including negative binomial model

random effects negative binomial model

and random parameters negative binomial model were developed by taking multi-mode failure probability and road factors as explanatory variables. Moreover

the relationship between multi-mode failure probability and single-car crashes was explored. Results show that among the three models

the random parameters negative binomial model outperformed the other two models. When the multi-mode failure probability was considered

the influence of road geometric factors on the single-car crashes was weakened. Except for two exposure variables

the multi-mode failure probability had the greatest impact on single-car crashes. The number of single-car crashes was approximately linearly related to the multi-mode failure probability

and the intercept of the fitting curve was not 0. The results can be used in the reliability design of highway.