ReliabilityProblem63

class ReliabilityProblem63(threshold=0.0, mu=0, sigma=1)

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, mu=0, sigma=1)

Creates a reliability problem RP63.

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

g(\boldsymbol{x}) = 0.1 \left(x_2^2 + x_3^2 + .... + x_{99}^2 + x_{100}^2\right) - x_1 - 4.5

for any \boldsymbol{x} \in \mathbb{R}^{10}.

We have:

X_i \sim \mathcal{N}(0, 1)

for i \in \{1, 2, ...,100\}.

Parameters:
thresholdfloat

The threshold.

mufloat

The mean of the Xi Normal distribution for i in {1, 2, …, 100}.

sigmafloat

The standard deviation of the Xi Normal distribution for i in {1, 2, …, 100}.

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.