Question 1

What is the structural reliability index β?

Accepted Answer

The reliability index β is a dimensionless measure of structural safety. For normally distributed resistance R and load S, β = (μ_R − μ_S) / √(σ_R² + σ_S²). A value of β = 3.0 corresponds to Pf ≈ 0.13%, and β = 4.0 to Pf ≈ 0.0032%. Building codes typically require β ≥ 3.5, while aerospace applications may require β ≥ 4–6.

Question 2

What is the difference between FORM and Monte Carlo simulation?

Accepted Answer

FORM (First-Order Reliability Method) linearizes the limit-state function at the design point to compute β analytically — it is fast and accurate for small Pf values. Monte Carlo simulation counts failures across random samples and becomes more accurate as the sample count increases, but requires many samples (N > 1/Pf) for rare events. Monte Carlo is preferred for nonlinear limit-state functions and non-standard distributions.

Question 3

When should I use the lognormal distribution?

Accepted Answer

Use lognormal distributions for variables that are strictly positive and right-skewed — such as material strengths, fatigue life, fracture toughness, or wind load intensities. The lognormal parameters are ζ = √ln(1+CoV²) and λ = ln(μ) − ζ²/2. FORM is applied in the standard normal space via the Rosenblatt transformation.

Question 4

How is this tool applied in structural and CAE engineering?

Accepted Answer

Input the mean and standard deviation of FEM-computed stresses together with material strength statistics to quantify the probability of failure. This supports compliance checks against ASME Boiler & Pressure Vessel Code (Section III), ISO 2394, and JCSS Probabilistic Model Code, as well as preliminary fatigue and fracture mechanics reliability assessments.

Structural Reliability Analysis & Probability of Failure

Theory