ReliabilityProblem91

class ReliabilityProblem91(threshold=0.0, mu1=0.07433, sigma1=0.005, mu2=0.1, sigma2=0.01, mu3=13.0, sigma3=60.0, mu4=4751.0, sigma4=48.0, mu5=-684.0, sigma5=11.0)

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=0.07433, sigma1=0.005, mu2=0.1, sigma2=0.01, mu3=13.0, sigma3=60.0, mu4=4751.0, sigma4=48.0, mu5=-684.0, sigma5=11.0)

Creates a reliability problem RP91.

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}))

for any \boldsymbol{x} \in \mathbb{R}^{5}.

g_1(\boldsymbol{x}) & = 0.847 + 0.96 x_2 + 0.986 x_3 - 0.216 x_4 \\ &\quad + 0.077 x_2^2 + 0.11 x_3^2 + \frac{7}{378} x_4^2 \\ &\quad - x_3 x_2 - 0.106 x_2 x_4 - 0.11 x_3 x_4 g_2(\boldsymbol{x}) & = \frac{84000 x_1}{\sqrt{x_3^2 + x_4^2 - x_3 x_4 + 3 x_5^2}} - 1 g_3(\boldsymbol{x}) & = \frac{84000 x_1}{|x_4|} - 1

We have :

  • x1 ~ Normal(mu1, sigma1),

  • x2 ~ Normal(mu2, sigma2),

  • x3 ~ Normal(mu3, sigma3),

  • x4 ~ Normal(mu4, sigma4),

  • x5 ~ Normal(mu5, sigma5).

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.

mu4float

The mean of the X4 gaussian distribution.

sigma4float

The standard deviation of the X4 gaussian distribution.

mu5float

The mean of the X5 gaussian distribution.

sigma5float

The standard deviation of the X5 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.