Abstract: The OOR (out of roundness) wheel is one of the main excitation sources causing the vehicle vibration. The OOR wheel is random, which indicates that the vibration behaviors of the vehicle cannot be comprehensively evaluated with a deterministic OOR wheel. A probability analysis approach is thusly proposed to obtain comprehensive random vibration characteristics of the vehicle considering the randomness of the OOR wheel. The probability model of the random OOR wheel is derived, in which the high-dimensional variables are expressed with as a few independent variables for the radius, amplitude and phase. A vehicle-track vertical coupled dynamics system considering OOR wheels is established. The DPIM (direct probability integral method) is developed to resolve the evolution process of excitation to response probabilities. The statistics of the vehicle random vibration are calculated. The effectiveness of the proposed approach is verified with a numerical case. The results show that the PDF (probability density function) shape of the vehicle random vibration excited by the Gaussian-distributed OOR wheel excitation no longer conforms to the Gaussian distribution and exhibits a right-skewed shape that significantly reduces the dynamic performance. As the mean or coefficient of variation of the OOR wheel amplitude increases linearly, the reliability of the vehicle dynamic performance exhibits a quadratic or double-sloping decrease. Moreover, the proposed approach can obtain the comprehensive vehicle random vibration characteristics for a comparable computational accuracy as Monte Carlo simulation, but with an improvement of at least an order of magnitude in calculation.