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Dependencies: PySTRA core.

Using SciPy distributions

Use a frozen SciPy distribution in a reliability model and check its parameters before running FORM and SORM.

Before you start: the introductory tutorial.

import pystra as ra
from scipy.stats import genextreme as gev

Define the limit-state function

def lsf(X1, X2, C):
    return X1 - X2 - C

Create the GEV variable and plot that it is defined as intended:

X2 = ra.ScipyDist("X2", gev(c=0.1, loc=200, scale=50))
X2.plot()

<Axes: >

Figure. The SciPy GEV probability density shows the distribution produced by its shape, location and scale parameters; these parameters are not its physical mean and standard deviation.

Now create the limit state and stochastic model objects, and add the variables

limit_state = ra.LimitState(lsf)

model = ra.StochasticModel()
model.add_variable(ra.Normal("X1", 500, 100))
model.add_variable(X2)
model.add_variable(ra.Constant("C", 50))

Suppress the console output

options = ra.FORMOptions()

Execute a FORM analysis

form = ra.FORM(
    model=model,
    limit_state=limit_state,
    options=options,
)
form_result = form.run()
print(form_result.summary())

FORM result
  Status                   converged
  Message                  Converged
  Failure probability      0.0249392
  Reliability index        1.961
  Iterations               5
  Limit-state evaluations  39

And then a SORM analysis (passing the existing FORM object for efficiency)

sorm = ra.SORM(model=model, limit_state=limit_state, form=form)
sorm_result = sorm.run()
print(sorm_result.summary())

SORM result
  Status                   converged
  Message                  Fitted
  Failure probability      0.0270706
  Reliability index        1.9257
  Fit                      curve
  FORM reliability index   1.961
  Pf, breitung             0.0270706
  Pf, modified breitung    0.0275476
  Limit-state evaluations  9

Interpretation

A SciPy shape, location and scale describe that distribution’s own parameterization; they are not generally its mean and standard deviation. Inspect the distribution before interpreting the reliability result.

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