Examples

Start with a first reliability analysis, then choose the methods or engineering workflow you need. The categories progress from introductory examples to advanced reliability methods and published benchmarks. Familiarity with Python and NumPy is assumed.

Choose a category below, or find a published problem in the Benchmark catalogue catalogue. Every notebook provides a download and a runnable bundle, including required helper files. Active-learning examples identify the optional al extra; their independent validation can cost more than the training run.

• Getting started
  • A first reliability analysis
  • Comparing FORM, SORM and simulation
  • Using SciPy distributions
  • Reliability with an external finite-element model
• Reliability methods and diagnostics
  • Simulation methods for reliability analysis
  • Reliability sensitivities
  • Direct differentiation of the limit state
  • Checking a FORM design point
  • Distribution adapters and analysis cost
• Systems and dependence
  • Dependence and probability transformations
  • System reliability
  • Rosenblatt ordering in system reliability
• Code calibration and engineering decisions
  • Load combinations and FBC processes
  • Code calibration using normalized reliability
  • Calibrating partial and combination factors
  • Steel-bar design decisions and LQI acceptability
  • Calibrating target-reliability tables
• Advanced methods: active learning and benchmarks
  • Active learning for reliability analysis
  • The hat-function benchmark
  • The 23-bar truss benchmark
  • PC-Kriging, bootstrap voting and importance sampling
  • Active learning with subset simulation

For Python background, see [Lutz2007] and [Langtangen2009].