SORM, Design Points, Subset Simulation, and Markov Chain Monte Carlo

The calculation of failure probabilities is one of the basic problems in structural reliability. But to understand the causes of failure, the pure calculation of probabilities is not sufficient. It is attempted to explain that this can be done using the concept of design points. Some important mathematical aspects of the subset simulation method are studied in detail. In this context, it is outlined that this approach is merely a Monte Carlo (MC) style numerical approximation attempt for finding the neighborhoods of the design points, i.e., a disguised importance sampling method. New methods based on first/second-order reliability methods (FORM/SORM) improved by suitable importance sampling methods are introduced. This approach combines the simplicity of the analytic concept with the flexibility of additional MC estimates. So the structuralist view based on design points, which was given up in favor of pure probability estimates by MC, is reintroduced.