Estimate a probability with Monte Carlo

In this example we estimate a probability by means of a simulation algorithm, the Monte-Carlo algorithm. To do this, we need the classes MonteCarloExperiment and ProbabilitySimulationAlgorithm. We consider the axial stressed beam example.

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

We load the model from the usecases module :

sm = stressed_beam.AxialStressedBeam()

We get the joint distribution of the parameters.

distribution = sm.distribution

The model is also stored in the data class :

model = sm.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.Less(), 0.0)

Create a Monte Carlo algorithm.

experiment = ot.MonteCarloExperiment()
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= 0.02936292270531395