# rare event analysis

Reliability analysis

## How large is the statistical uncertainty in the estimate of a Monte Carlo simulation?

For a given probability of failure, the variance and coefficient of variation of the Monte Carlo estimate can be evaluated analytically. From this, the total number of samples required to maintain a target coefficient of variation can be deduced.

Reliability analysis

## Why is Monte Carlo simulation so robust?

Monte Carlo simulation is a very robust structural reliability method because its performance depends solely on the total number of samples and the underlying probability of failure.

Reliability analysis

## How to use Monte Carlo simulation for reliability analysis?

Monte Carlo simulation divides the number of samples with system failure by the total number of random samples generated to estimate the probability of failure in a reliability analysis.

Reliability analysis

## What is a limit state function?

The limit state function distinguishes undesired from acceptable system behavior. It is used in structural reliability analysis to define a failure criterion.