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.

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Reliability analysis

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

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Reliability analysis

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

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Reliability analysis

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.

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Reliability analysis

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

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Reliability analysis

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

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Reliability analysis

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

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

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Reliability analysis

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.

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Reliability analysis

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.

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Reliability analysis

Even if Monte Carlo simulation returns not a single sample in the failure domain, we can still quantify the uncertainty about whether a specified target reliability level is maintained.

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Reliability analysis

We explain a Bayesian post-processing step for MCS. It is ideally suited to quantify the uncertainty and to evaluate credible intervals for the probability of failure.

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Reliability analysis

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.

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