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Based on the reliability theory, this paper gave the expression of the "failure-non failure"state of the urban road traffic unit and the traffic network and analyzed the change law of their states; analyzed the time distribution of the link unit and the traffic network from the observed starting point t0 to the "first failure state". Based on these, it deduced the failure probability, average failure time, failure rate and conditional length of failure time of the urban road unit and traffic network, it also gave the method of model calibration. It took a road traffic network that composed of five road units in a core city of China by an example, fitted and checked the first failure time of the road units and the traffic network, also compared the model calculation results with the actual observation results. The results show that it is better to use logarithmic normal distribution to fit the first failure time, and the calculation results of the model are very close to the actual observation results, which shows that the model has good practicability. [ABSTRACT FROM AUTHOR]