ReliabilityProblem60

class ReliabilityProblem60(threshold=0.0, mu1=2200, sigma1=220, mu2=2100, sigma2=210, mu3=2300, sigma3=230, mu4=2000, sigma4=200, mu5=1200, sigma5=480)

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=2200, sigma1=220, mu2=2100, sigma2=210, mu3=2300, sigma3=230, mu4=2000, sigma4=200, mu5=1200, sigma5=480)

Creates a reliability problem RP60.

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

g(\boldsymbol{x}) = \min(g_1(\boldsymbol{x}), g_{11}(\boldsymbol{x}))

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

g_1(\boldsymbol{x}) &= x_1 - x_5 g_2(\boldsymbol{x}) &= x_2 - \frac{x_5}{2} g_3(\boldsymbol{x}) &= x_3 - \frac{x_5}{2} g_4(\boldsymbol{x}) &= x_4 - \frac{x_5}{2} g_5(\boldsymbol{x}) &= x_2 - x_5 g_6(\boldsymbol{x}) &= x_3 - x_5 g_7(\boldsymbol{x}) &= x_4 - x_5 g_8(\boldsymbol{x}) &= \min(g_5(\boldsymbol{x}), g_6(\boldsymbol{x})) g_9(\boldsymbol{x}) &= \max(g_7(\boldsymbol{x}), g_8(\boldsymbol{x})) g_{10}(\boldsymbol{x}) &= \min(g_2(\boldsymbol{x}), g_3(\boldsymbol{x}), g_4(\boldsymbol{x})) g_{11}(\boldsymbol{x}) &= \max(g_{10}(\boldsymbol{x}), g_9(\boldsymbol{x}))

We have :

  • x1 ~ LogNormalMuSigma(mu1, sigma1),

  • x2 ~ LogNormalMuSigma(mu2, sigma2),

  • x3 ~ LogNormalMuSigma(mu3, sigma3),

  • x4 ~ LogNormalMuSigma(mu4, sigma4),

  • x5 ~ LogNormalMuSigma(mu5, sigma5).

Parameters:
thresholdfloat

The threshold.

mu1float

The mean of the LogNormal random variable X1.

sigma1float

The standard deviation of the LogNormal random variable X1.

mu2float

The mean of the LogNormal random variable X2.

sigma2float

The standard deviation of the LogNormal random variable X2.

mu3float

The mean of the LogNormal random variable X3.

sigma3float

The standard deviation of the LogNormal random variable X3.

mu4float

The mean of the LogNormal random variable X4.

sigma4float

The standard deviation of the LogNormal random variable X4.

mu5float

The mean of the LogNormal random variable X5.

sigma5float

The standard deviation of the LogNormal random variable X5.

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.