Optimization-assisted Reliability Analysis

Reliability-based design optimization (RBDO) is the classic academic framing — a bilevel program where the outer loop optimizes design variables and the inner loop evaluates failure probability. Optimization-assisted reliability analysis is a broader term covering the same idea but also encompasses scenarios where optimization helps the reliability solver itself (e.g., finding the design point in FORM via constrained optimization). The practical workflow is essentially the same.

FORM is fast (often just tens of function evaluations per reliability call) and works well for smooth, mildly nonlinear limit states with a single dominant failure mode. Use Monte Carlo — or importance sampling — when the limit state is highly nonlinear, when multiple failure modes interact, or when you need to verify a FORM result. For expensive simulation models, replace direct Monte Carlo with a surrogate (response surface, Kriging) to keep the computational cost manageable.

Target values are typically derived from regulatory standards, structural codes (e.g., ISO 2394, JCSS Probabilistic Model Code), or risk-based decision frameworks. Common engineering targets range from 10⁻³ to 10⁻⁷ per year depending on consequence severity and component inspectability. Avoid setting targets that are more precise than your input data can support.

Yes, but with caution. Bayesian updating allows you to combine sparse experimental data with prior engineering knowledge to estimate distribution parameters. Be explicit about parameter uncertainty (epistemic uncertainty) and consider sensitivity analysis to assess how much the final design changes with plausible alternative distribution assumptions. If data are very scarce, a conservative deterministic safety-factor approach may be more defensible.

Dedicated tools include FERUM, OpenRELACS, and CALREL for reliability calculations; commercial platforms such as ANSYS Mechanical, Abaqus, and OptiStruct offer built-in RBDO modules. General-purpose scientific computing environments (Python with scipy/openturns, MATLAB) are widely used for custom implementations. For large finite-element models, surrogate-model toolboxes (UQLab, Dakota) are the standard approach.