Sequential and Decoupled Reliability Analysis applied to time-dependent engineering systems

Abstract

Abstract Traditionally, reliability analysis neglects the influence of time, leading to inaccurate predictions for systems under progressive degradation and variable loads. However, addressing time dependency is of major significance, as material aging and cumulative damage dynamically alter the system’s condition, increasing the probability of failure throughout its operational lifespan. Time-dependent (or time-variant) reliability analysis addresses this challenge, as time directly affects failure probability. This paper proposes and evaluates two methodologies: Sequential Reliability Analysis (SRA) and Decoupled Reliability Analysis (DRA). SRA transforms the time-dependent problem into an equivalent time-independent one by discretizing time, using a metamodel to approximate the failure probability profile, and performing a one-dimensional search for the optimal value. In this method, reliability analysis is required at each discretized time point. Conversely, DRA also removes time dependency but does so by replacing the time variable with a metamodel dependent on random variables, requiring only one reliability analysis. Both methodologies were validated through mathematical and engineering case studies. The results demonstrate that both provide accurate failure probability estimates, with errors below 2% when compared to reference solutions or Monte Carlo Method (MCM) results. Additionally, the DRA approach achieved a computational cost reduction of up to 99.8% relative to the traditional method. These findings confirm the effectiveness and efficiency of the proposed approaches for time-dependent reliability analysis in engineering applications.