On the basis of the dynamic equations of the Jeffcott rotor-stator model with imbalance, the reliability of the rotor-stator systems with rubbing is examined. A statistical fourth moment method is developed to determine the first four moments of system response and state function. The distribution function of the system state function is approximately determined by the standard normal distribution functions using the Edgeworth series technique. The reliability is obtained and the effect on reliability of shaft stiffness and damping, stator stiffness and damping, radial clearance and stator radial stiffness is studied. Numerical results are also presented and discussed.