This function calculates the probability of failure for a given reliability index using a standard normal cumulative distribution function. It performs the calculation by integrating the probability density function (PDF) of a standard normal distribution.

pf_value = pf_equation(beta)

Input variables

Name	Description	Type
beta	Reliability index	Float

Output variables

Name	Description	Type
pf_value	Probability of failure	Float

Example 1

Use pf_equation function to calculate the probability of failure for a reliability index of 3.5.

# Library
from parepy_toolbox import pf_equation

# Calc pf
beta = 3.5
pf = pf_equation(beta)
print(f"Probability of failure {pf:.5e}")

Output details.

Probability of failure 2.32629e-04