Choosing a reliability method#

Start with the failure event, its joint probability model and the cost of one limit-state evaluation. A converged algorithm can still give an inaccurate approximation. Use an independent reference or a second method where feasible.

Starting points and checks#
Method	Useful starting point	What to check
`FORM`	Smooth response with a dominant failure region; economical initial study.	Convergence, gradients, competing design points and local approximation error.
`SORM`	Curvature near a converged FORM design point matters.	Curvature and fitting validity; additional failure regions remain a concern.
`CrudeMonteCarlo`	Affordable evaluations; a direct check on the physical failure event.	Enough observed failures and reported sampling precision.
`ImportanceSampling`	A FORM design point identifies an important failure region.	Proposal coverage, weight variability and regions away from that point.
`LineSampling`	A useful direction is available and line intersections can be found.	Direction choice, root searches and boundary geometry along lines.
`SubsetSimulation`	Rare events for which direct Monte Carlo is too costly.	Threshold progression, chain mixing and variability across independent runs.
`SystemFORM`	A system can be described through component limit states and topology.	Every component’s convergence and a shared transformation; validate the original event.
`ActiveLearning`	Expensive evaluations justify fitting and enriching a surrogate.	Training budget, stopping reason, independent validation and final estimator uncertainty.

A practical sequence#

Verify units, the sign of failure and the joint distribution using Specifying a reliability model and Copulas and isoprobabilistic transformations.
For a smooth component, run Running FORM and SORM and inspect the design point. For a system, preserve the topology and use System reliability.
Check the approximation with Estimating failure probability by simulation or an independent integral on a tractable benchmark. A small FORM/SORM difference alone is insufficient.
When evaluations dominate cost, consider Active-learning methods and literature, retaining an evaluation budget for independent validation.

After checking the FORM solution, use Computing reliability sensitivities to quantify local changes in the reliability index with marginal parameters and, where supported, physical correlation coefficients.

Discontinuous functions can be sampled directly when affordable, but ordinary FORM and SORM require local derivatives. Strong nonlinearity, multiple failure regions and transformation ordering require particular care. PySTRA normally uses independent standard normal coordinates; see Notation and probability spaces. Beyond a reliability index of about 8 the probabilities involved fall below \(10^{-15}\); Working at high reliability describes how the methods behave there.

Continue: Benchmark catalogue · Interpreting results and convergence · Reliability algorithms and results