Time-dependent reliability analysis with series expansion and equivalent-plane approach

Abstract. Developing highly efficient and accurate methodologies is a central challenge in the field of time-dependent reliability. In this paper, a time-dependent-reliability analysis method that couples series expansion with the equivalent-plane approach is proposed. The first-order reliability method (FORM) is applied to evaluate the reliability on a discretized time instant, and expansion optimal linear estimation (EOLE) represents the stochastic process by series expansion and constructs its correlated representation. The equivalent-plane approach (EPA) is used to aggregate the discretized failure events and to estimate the time-dependent failure probability over the considered period. Three numerical examples demonstrate that the proposed method achieves close agreement with Monte Carlo simulation benchmarks while requiring far fewer limit state evaluations.