On the basis of the dynamic equations of the Jeffcott rotor–stator model with imbalance, the reliabilitysensitivity 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 approximatelydetermined by the standard normal distribution functions using the Edgeworth series technique. The reliabilityand reliabilitysensitivityare obtained and the effect on reliabilityand reliabilitysensitivity of shaft stiffness and damping, stator stiffness and damping, radial clearance and stator radial stiffness is studied. Numerical results are also presented and discussed.

Based on the generalized probabilistic finite element method, this paper presents anapproximate solution technique for general multi-degree-of-freedom nonlinear random vibrationsystems with random parameters. The fourth-moment technique, maximum entropy theory andincomplete probability information theory are employed to systematically develop a reliabilityanalysis method for dynamic random structural systems with correlation failure modes underunavailable joint probability density functions of basic random variables. The first passage problemof multi-degree-of-freedom nonlinear random vibration systems is solved.

Techniques from perturbation method and reliability-based design theory are employed to present the practical and effective method for the reliability-based design of gear pairs. The theoretical formulae of reliability-based design of gear pairs are obtained. The corresponding program can be used to obtain the reliability-based design parameters of gear pairs accurately and quickly.

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.

This paper extends the stochastic perturbation method to vector-valued and matrix-valued functions. The numerical method for the response and reliability of uncertain structures is formulated using matrix calculus, Kronecker algebra and perturbation theory. Random variables and system derivatives are conveniently arranged into two-dimensional matrices and generalized mathematical formulae are obtained. The results derived are easily amenable to computational procedures.