# Resources

Resources
covered subject areas

Expand your knowledge through our resources. Try our online tools and start reading our articles about probabilistic modeling, machine learning, risk assessment, uncertainty quantification and other fundamental topics. Here are the resources you need to get started dealing with uncertainties that arise in your day-to-day projects.

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Probabilistic modeling

## Poisson process: post-processing

Use our web app to quantify the uncertainty about the rate of a Poisson process based on observing a specific number of event occurrences within a given time.
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Probabilistic modeling

## Poisson process: estimate required experiment duration

Use our web app to decide how long an experiment needs to run in order to demonstrate that your system is reliable.
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Probabilistic modeling

## For how long do you need to observe a Poisson process to ensure that its rate is smaller than a specified threshold?

With assumptions on how many events will occur, one can determine the time required to demonstrate that the rate is below a target value with a specified credible level.

Probabilistic modeling

## What conclusions can we draw if we did not observe any occurrences of a Poisson process within a given time interval?

Using a Bayesian post-processing strategy, the uncertainty about the rate of a Poisson process can be fully quantified even if no occurrences were observed.

Machine learning

## Research paper: Speed-power models – a Bayesian approach

A data-driven approach is used to learn speed-power curves probabilistically. These models can then be used to assess the performance of a vessel.

Reliability analysis

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

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

Probabilistic modeling

## Does it make a difference whether or not a discretized Poisson process is used in Bayesian post-processing?

Even though the underlying posterior distributions are of different type, the results will be the same if the rate of the Poisson process is sufficiently small and weakly informative and consistent priors are used.

Probabilistic modeling

## What prior to use when learning the rate of a Poisson process?

A weakly informative prior that follows a Gamma distribution with shape parameter 1 and rate parameter 2 is a suitable choice for many problems. Working with informative prior distributions requires careful handling and a close look at the quantiles.

Machine learning

## Research paper: Data-driven predictive maintenance for gas distribution networks

A data-driven approach that uses all available information to forecast the defect rate of pipes in a gas distribution network is presented.

Probabilistic modeling

## How to quantify the uncertainty about the rate of a Poisson process?

We explain a Bayesian post-processing step for learning the rate of a Poisson process. It is ideally suited to quantify the uncertainty and to evaluate credible intervals.

Probabilistic modeling

## What is a Poisson process?

A Poisson process is used to model the occurrence of independent random events along a continuous axis. It is a very important stochastic process in probabilistic modeling.

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.
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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.

Probabilistic modeling

## What is the difference between credible and confidence intervals?

Credible intervals express our belief that the true underlying value is contained within the interval conditional on the conducted simulation run. Contrary to that, confidence intervals are only meaningful for a large number of repeated simulation runs.

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.

Reliability analysis

## How to interpret the outcome of a Monte Carlo simulation if no failures occurred?

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.

STRUREL

## What is STRUREL?

STRUREL is a collection of software modules for probabilistic modeling in structural engineering. It offers state-of-the-art numerical methods for structural reliability analysis.

STRUREL

## How to employ a MATLAB limit state function in STRUREL?

Integrating a MATLAB model into a reliability analysis is very straightforward in STRUREL. We explain the basic steps using a simple toy example.

STRUREL

## How to employ a Python limit state function in STRUREL?

Integrating a Python model into a reliability analysis is very straightforward in STRUREL. We explain the basic steps using a simple toy example.

Reliability analysis

## How to assess the uncertainty in the outcome of a Monte Carlo simulation?

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.

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.