How to Perform a FORM Reliability Analysis
The procedure for a First-Order Reliability Method analysis — transforming to standard-normal space, finding the design point, computing the reliability index and the failure probability.
When to use this guide
Use this guide when performing a FORM analysis to compute a reliability index and failure probability without Monte Carlo sampling.
Required inputs
- Limit-state function g(X) with defined random variables
- Distributions for each random variable
- Engineering model that evaluates g for a given X
Step-by-step method
- Transform each random variable to standard normal space (Rosenblatt or Nataf transformation)
- Set up the optimisation: minimise the distance from the origin to the limit-state surface in standard-normal space
- Run the optimisation to find the design point (most probable failure point)
- Compute the reliability index beta = distance from origin to design point
- Compute the approximate failure probability: Pf = Phi(-beta)
- Extract sensitivity factors: the direction cosines of the design point indicate each variable's contribution
- Check linearity: assess the curvature of the limit state at the design point — if significant, consider SORM
- Verify: compare Pf with a Monte Carlo estimate if feasible
Checks
- The design point is physically plausible — the combination of input values makes engineering sense
- The optimisation has converged to a stable design point
- Multiple starting points give the same design point (no multiple design points missed)
- Sensitivity factors sum to approximately one (normalised)