Robustness of Subset Simulation to Functional Forms of Limit State Functions in System Reliability Analysis: Revisiting and Improvement

With the development of computing technologies, computer-based simulation methods have gained increasing attention in reliability analysis of engineering systems, among which subset simulation (SS) provides a robust yet efficient tool for exploring system rare failure events and evaluating system reliability. However, the component limit state functions (LSFs) of a system can be formulated in different forms (e.g., linear, exponential, and scaled), depending on mathematical modeling of the engineering systems concerned. This affects the system LSF and the performance of SS, and may lead to inconsistent system reliability analysis results. This study systematically explores effects of the functional form of component LSFs on the performance of SS in system reliability analysis and accounts for such effects from the perspective of sampling procedures. It is found that the efficient generation of conditional samples during SS, which is pivotal to the success of SS, is affected by the functional form of component LSFs in the system concerned. The performance of SS can be sensitive to the functional form of component LSFs. Normalizing component LSFs eliminate the effects of scaled LSFs on the performance of SS, but it does not improve the robustness (insensitivity) of SS in system reliability analysis involving exponential LSFs that are nonlinear. Understanding the effects of component LSFs on the performance of SS, a generalized SS (GSS) algorithm is proposed for system reliability analysis, which is robust to different functional forms of component LSFs provided that the functional transformation of component LSFs does not change their monotonicity and failure domains. Numerical examples and a real engineering example showed that the proposed algorithm is more robust to the functional form of component LSFs in system reliability analysis than standard SS.