ReliabilityProblem55

class ReliabilityProblem55(threshold=0.0, a=[-1.0, -1.0], b=[1.0, 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, a=[-1.0, -1.0], b=[1.0, 1.0])

Creates a reliability problem RP55.

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

g(boldsymbol{x}) = min(g_1(boldsymbol{x}), g_2(boldsymbol{x}),

g_3(boldsymbol{x}), g_4(boldsymbol{x}))

for any \boldsymbol{x} \in \mathbb{R}^2 where:

g_1(\boldsymbol{x}) & = 0.2 + 0.6 (x_1 - x_2)^4 - \frac{x_1 - x_2}{\sqrt{2}} g_2(\boldsymbol{x}) & = 0.2 + 0.6 (x_1 - x_2)^4 + \frac{x_1 - x_2}{\sqrt{2}} g_3(\boldsymbol{x}) & = (x_1 - x_2) + \frac{5}{\sqrt{2}} - 2.2 g_4(\boldsymbol{x}) & = (x_2 - x_1) + \frac{5}{\sqrt{2}} - 2.2

We have:

  • x1 ~ Uniform(a[0], b[0]) and

  • x2 ~ Uniform(a[1], b[1]).

Parameters:
thresholdfloat

The threshold.

bsequence of floats

The list of two items representing the upper bounds of the Uniform distribution.

asequence of floats

The list of two items representing the lower bounds of the Uniform 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.