System reliability-based design optimization using the MPP-based dimension reduction method

The system probability of failure calculation of the series system entails multi-dimensional integration, which is very difficult and numerically expensive. To resolve the computational burden, the narrow bound method, which accounts for the component failures and joint failures between two failure modes, has been widely used. For the analytic calculation of the component probability of failure, this paper proposes to use the most probable point (MPP)-based dimension reduction method (DRM). For the joint probability of failure calculation, three cases are considered based on the convexity or concavity of the performance functions. Design sensitivity analysis for the system reliability-based design optimization (RBDO), which is the major contribution of this paper, is carried out as well. Based on the results of numerical examples, the system probability of failure and its sensitivity calculation show very good agreement with the results obtained by Monte Carlo simulation (MCS) and the finite difference method (FDM).