Structural cumulative damage is closely related to the duration of the structural stress process exceeding safety threshold. This work studies certain types of structural stress stochastic processes with Wiener characteristics in engineering. Based on the probability analysis of multiple threshold crossings for Wiener process, this work advances structural fatigue reliability analysis to capture the impact of the duration of random response process exceeding threshold on the structural cumulative damage. First, the structure fatigue cumulative damage index considering random response crossing-threshold duration is derived based on the assumption that cumulative damage is linear with respect to crossing-threshold duration. Then, according to the relationship between the fatigue cumulative damage index and the crossing number of stress response process and the damage threshold, the structural fatigue reliability is expressed as a probability expression that the crossing number does not exceed a certain value. Finally, the probability distribution of the crossing number is analyzed by Monte Carlo method, and the structural fatigue reliability is calculated using MATLAB program compiled. The fatigue reliabilities of a key component of subway bogie under different operation periods are analyzed using the proposed method which verifies its correctness.