Reliability Index Reference

Quick reference for the reliability index beta, its relationship to failure probability and illustrative beta-to-Pf conversion values.

Probabilistic & Reliability3 min read

referencereliability indexbetafailure probabilityconversion

Key relationship

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

Illustrative conversions:
  beta = 2.0 → Pf = 2.3e-2
  beta = 2.5 → Pf = 6.2e-3
  beta = 3.0 → Pf = 1.4e-3
  beta = 3.5 → Pf = 2.3e-4
  beta = 4.0 → Pf = 3.2e-5
  beta = 4.5 → Pf = 3.4e-6
  beta = 5.0 → Pf = 2.9e-7

Note

These conversions are exact for linear limit states with normal variables. For nonlinear limit states or non-normal variables, the relationship is approximate (FORM) or requires curvature correction (SORM). No universal target beta is appropriate for all applications.