# rare event analysis

Reliability analysis

## What is the failure domain in a reliability analysis?

The failure domain consists of all samples for which the limit-state function becomes smaller or equal than zero.

Reliability analysis

## What is FORM?

FORM is a structural reliability analysis method that approximates the probability of failure by linearizing the limit state function around the design point.

Probabilistic modeling

## What is the underlying standard Normal space?

The uncertain model parameters are transformed into independent standard Normal random variables. For the performance and stability of numerical algorithms, performing such a transformation step is sometimes preferable.

Reliability analysis

## What is the most likely failure point?

It is the point in the failure domain that has the smallest distance to the origin in standard Normal space. This point is also referred to as design point.

Reliability analysis

## How is the reliability index linked to the probability of failure?

The reliability index is directly linked to the probability of failure through the negative of the inverse CDF of the standard Normal distribution.

Reliability analysis

## What is the 'safety margin' in structural reliability analysis?

The difference between the capacity and the demand is the safety margin.

Reliability analysis

## What is the 'basic structural reliability problem'?

When the limit state function can be expressed as the difference between capacity and demand, the problem is sometimes referred to as basic reliability problem.

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Reliability analysis

## Post-processing of Monte Carlo simulation

Use our web app to quantify the uncertainty about the probability of failure based on a conducted Monte Carlo simulation.
try it ...

Reliability analysis

## Why should you avoid Normal confidence intervals for Monte Carlo simulation?

The underlying distribution can be highly skewed, even if the total number of samples in the Monte Carlo simultion is very large. This is why the Normal approximation often performs poorly in practice.

Reliability analysis

## Why to avoid the coefficient of variation in the context of a Monte Carlo simulation?

The distribution quantifying the uncertainty about the probability of failure can be highly skewed, even for a large number of samples. The coefficient of variation is easier to interprete for symmetric distributions.

STRUREL

## How to employ Monte Carlo simulation in COMREL?

After a brief overview of Monte Carlo simulation (MCS) for structural reliability, we explain the details of conducting a MCS in COMREL.