Estimate a probability using randomized QMCΒΆ

In this example we are going to estimate a failure probability on the cantilever beam.

```from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
```

We load the data class containing the probabilistic modeling of the beam.

```from openturns.usecases import cantilever_beam as cantilever_beam
cb = cantilever_beam.CantileverBeam()
```

We load the joint probability distribution of the input parameters :

```distribution = cb.distribution
```

We load the model as well,

```model = cb.model
```

We create the event whose probability we want to estimate.

```vect = ot.RandomVector(distribution)
G = ot.CompositeRandomVector(model, vect)
event = ot.ThresholdEvent(G, ot.Greater(), 0.3)
```

Define the low discrepancy sequence.

```sequence = ot.SobolSequence()
```

Create a simulation algorithm.

```experiment = ot.LowDiscrepancyExperiment(sequence, 1)
experiment.setRandomize(True)
algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
algo.setMaximumCoefficientOfVariation(0.05)
algo.setMaximumOuterSampling(int(1e5))
algo.run()
```

Retrieve results.

```result = algo.getResult()
probability = result.getProbabilityEstimate()
print('Pf=', probability)
```

Out:

```Pf= 0.0
```

Total running time of the script: ( 0 minutes 1.028 seconds)

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