According to the relationship of forcing frequency to natural frequency, the quasi-failure model and thequasi-failure probability for the random continuous vibration systems are defined, and the frequencyreliability analysis method for avoiding the resonant is Ixesented. By using the vibration theory and thereliability technique, the quasi-failure analysis method for resoramt problem for the random continuousvibration systems is studied.

The dynamic equations of the Jeffcott rotor with imbalance are concerned. The reliabilityof rotor systems with rubbing is examined. A statistical fourth moment method is developedto determine the first four moments of the system response and the state function.The distribution function of the system state function is approximately determined byusing the Edgeworth series technique. Its reliability is obtained. The effect on the reliabilityof the shaft stiffness, the external damping coefficient, the degree of imbalance andthe stator stiffness is studied. Numerical results are also presented and discussed.

This paper extends the probabilistic finite element method (PFEM) to vector-valued and matrix-valued functions using techniques from matrix calculus and Kronecker algebra, and presents the PFEM in Kronecker notation for linear mad nonlinear continua. The results derived are easily amenable to computa-tional procedures.

Techniques from the perturbation method, the Edgeworth series, the reliability-based design theory and the sensitivity analysis approach are employed to present a practical and efficient method for the reliability sensitivity of automobile components with arbitrary distribution parameters. On the condition of first four moments of Original random variables known, the reliability sensitivity theory and case studies are researched. The respective program can be used to obtain the reliability sensitivity of automobile components with arbitrary distribution parameters accurately and quickly.