ReliabilityProblem77

class ReliabilityProblem77(threshold=0.0, mu1=10.0, sigma1=0.5, mu2=0.0, sigma2=1.0, mu3=4.0, sigma3=1.0)

Methods

computeBeta()

Return the beta of the reliability problem.

getEvent()

Return the event.

getName()

Return the name of the problem.

getProbability()

Return the probability.

toFullString()

Convert the object into a string, with full details.
__init__(threshold=0.0, mu1=10.0, sigma1=0.5, mu2=0.0, sigma2=1.0, mu3=4.0, sigma3=1.0)

Creates a reliability problem RP77.

The event is \{g(\boldsymbol{X}) < \text{threshold}\} where

g(\boldsymbol{x}) = \begin{cases} x_1 - x_2 - x_3 & \text{ if } x_3 \leq 5.0, \\ x_3 - x_2 & \text{otherwise}, \end{cases}

for any \boldsymbol{x} \in \mathbb{R}^{3}. We have :

& X_1 \sim \mathcal{N}(\mu_1, \sigma_1^2), \\ & X_2 \sim \mathcal{N}(\mu_2, \sigma_2^2), \\ & X_3 \sim \mathcal{N}(\mu_3, \sigma_3^2).

Parameters:
thresholdfloat

The threshold.

mu1float

The mean of the X1 gaussian distribution.

sigma1float

The standard deviation of the X1 gaussian distribution.

mu2float

The mean of the X2 gaussian distribution.

sigma2float

The standard deviation of the X2 gaussian distribution.

mu3float

The mean of the X3 gaussian distribution.

sigma3float

The standard deviation of the X3 gaussian distribution.

computeBeta()

Return the beta of the reliability problem.

This is the quantile of the probability of a standard gaussian distribution.

Parameters:
None.
Returns:
beta: float

The beta of the problem.

getEvent()

Return the event.

Parameters:
None.
Returns:
event: ot.ThresholdEvent

The event.

getName()

Return the name of the problem.

Parameters:
None.
Returns:
name: str

The name of the problem.

getProbability()

Return the probability.

Parameters:
None.
Returns:
probability: float

The probability of the event.

toFullString()

Convert the object into a string, with full details.

Parameters:
None.
Returns:
s: str

The string of the problem.