Benchmark catalogue

These examples connect a physical or analytical problem to its published source and an independent check. Open the linked notebook for parameters, citations, assumptions and executable comparisons. Source notation and reported rounding are retained where needed. The table describes validation scope, not a ranking of algorithms.

Reusable reference problems

Example	Source and assumptions	Reference and interpretation
A first reliability analysis	Independent normal resistance minus load; a teaching problem.	Exact normal tail. FORM is exact for the planar normal-space boundary.
Simulation methods for reliability analysis	Hypersphere and parabolic limit states; see [Schueller2007] and [Breitung1984].	Chi-square tail and independent integration; compare sampling methods and local approximation error.
Rosenblatt ordering in system reliability	Meinen–Steenbergen’s identical-event system with Gaussian or Frank dependence.	Direct integration and original-event Monte Carlo. The notebook explains the apparently interchanged dependent-case probabilities in the paper.
System reliability	Daniels bundle, component topology, cut sets and Ditlevsen bounds.	Published worked values, exact event enumeration and original-system Monte Carlo check different parts of the implementation.
Active learning for reliability analysis	Lognormal beam and four-branch system; active-learning literature benchmarks.	Analytical beam probability and independent quadrature for the system; assess classification as well as probability.
The hat-function benchmark	Explicit UQLab hat definition; review comparison in Literature benchmark definitions and provenance.	Independent integral and exact cubic representation check. Exact polynomial recovery does not generalize to arbitrary boundaries.
The 23-bar truss benchmark	Published 23-bar truss with ten independent inputs [MarelliSudret2018].	Independently checked mechanics and conditional integration; distinguish local, sampling and surrogate errors.
PC-Kriging, bootstrap voting and importance sampling	Four-branch system, lognormal beam and two normal tails.	PC-Kriging, bootstrap voting and importance sampling checked against independent references.
Active learning with subset simulation	Linear tail and multiple failure regions.	Exact normal-tail probabilities and replicated conditional sampling diagnostics.
Steel-bar design decisions and LQI acceptability	Schubert–Faber JCSS steel-bar decision.	Compare published decision points with economic, target-table and marginal LQI criteria.
Calibrating target-reliability tables	LQI and Rackwitz/Steenbergen normalized target models.	Compare representative trends with published rounded classes; this does not reproduce every class exactly.

The active-learning overview, extensions and subset-simulation notebooks require pystra[al] for Kriging. The hat and truss PCE examples use the core installation; their runnable bundles include literature_benchmarks.py. Execution cost depends on training, independent validation and sampling budgets, as well as the machine and numerical libraries; each notebook states its actual settings.

For detailed source definitions and comparison discrepancies, see Literature benchmark definitions and provenance.

Continue: Examples · Choosing a reliability method · References · Citing PySTRA and its methods