# Reliability & Sensitivity¶

## Central dispersion¶

Evaluate the mean of a random vector by simulations

Analyse the central tendency of a cantilever beam

Estimate moments from Taylor expansions

## Reliability¶

Estimate a probability with Latin Hypercube Sampling

Estimate a probability with Monte Carlo

Use a randomized QMC algorithm

Use the Adaptive Directional Stratification Algorithm

Use the post-analytical importance sampling algorithm

Use the Directional Sampling Algorithm

Estimate a flooding probability

Specify a simulation algorithm

Use the Importance Sampling algorithm

Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability

Exploitation of simulation algorithm results

Use the FORM algorithm in case of several design points

Non parametric Adaptive Importance Sampling (NAIS)

Use the FORM - SORM algorithms

Test the design point with the Strong Maximum Test

Time variant system reliability problem

Axial stressed beam : comparing different methods to estimate a probability

Create unions or intersections of events

An illustrated example of a FORM probability estimate

Cross Entropy Importance Sampling

## Reliability processes¶

Create an event based on a process

Estimate a process-based event probability

Estimate Sobol indices on a field to point function

## Sensitivity analysis¶

Parallel coordinates graph as sensitivity tool

Estimate Sobol’ indices for a function with multivariate output

Sobol’ sensitivity indices from chaos

The HSIC sensitivity indices: the Ishigami model

Example of sensitivity analyses on the wing weight model

## Design of experiments¶

Create a composite design of experiments

Create a Monte Carlo design of experiments

Probabilistic design of experiments

Create a random design of experiments

Create mixed deterministic and probabilistic designs of experiments

Create a design of experiments with discrete and continuous variables

Deterministic design of experiments

Create a deterministic design of experiments

Various design of experiments in OpenTURNS

Generate low discrepancy sequences

Optimize an LHS design of experiments

Merge nodes in Smolyak quadrature