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 proposes the application of reliability-based optimization and robust design methods of a coil tube-spring. The perturbation method, the Edgeworth series, the reliability-based optimization, the reliability sensitivity technique, and the robust design method are employed to present practical and effective approaches of reliability-based optimization and robust design for coil tube-spring with non-normal distribution parameters, on the condition of the known first four moments of the original random variables. Theoretical formulae for reliability-based optimization and robust design are obtained. The respective programmes can be used to obtain the reliability-based optimization and robust design parameters of a coil tube-spring with non-normal 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.

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.