Langford Analytic · Knowledge Base

Reliability Index / Failure Probability Conversion Calculator

Convert between a reliability index (beta) and a failure probability (Pf) using the standard normal CDF relationship.

Probabilistic & Reliability2 min read
calculatorreliability indexbetafailure probabilityconversion

Calculator

Pf = Phi(-beta)
beta = -Phi^{-1}(Pf)

where:
  beta = reliability index
  Pf = probability of failure
  Phi = standard normal CDF
  Phi^{-1} = inverse standard normal CDF

Enter beta to compute Pf, or enter Pf to compute beta.

Assumptions

  • The relationship is exact for linear limit states with normal variables
  • For nonlinear or non-normal cases, the relationship is approximate (FORM)

Limitations

This conversion assumes the FORM approximation is valid. For nonlinear limit states with significant curvature, SORM corrections apply. No universal target beta is appropriate for all structures.