Running FORM and SORM

FORM returns a convergence record and a local approximation to failure probability. Start with the A first reliability analysis example, then use Comparing FORM, SORM and simulation to compare approximations on a nonlinear model.

Run and inspect FORM

import pystra as ra

model = ra.StochasticModel()
model.add_variable(ra.Normal("R", 10.0, 1.0))
model.add_variable(ra.Normal("S", 5.0, 1.0))
response = ra.LimitState(lambda R, S: R - S)
form = ra.FORM(model, response)
result = form.run()
assert result.converged, result.message
assert result.failure_probability is not None
design = dict(zip(result.variable_names, result.design_point_x))
assert abs(design["R"] - design["S"]) < 1e-3

Inspect convergence before reading the probability or design point. Check that the physical point lies on the intended boundary and that its units and signs make sense. Convergence only establishes the local numerical solution: it does not rule out other important failure regions. See Strong Maximum Test and Troubleshooting reliability analyses for further checks.

Reuse the analysis in SORM

Pass the completed FORM analysis to SORM so it can reuse the design point and transformation. The immutable FORMResult is a reporting record; the form= argument requires the analysis object.

sorm_result = ra.SORM(model, response, form=form).run()
assert sorm_result.converged
probability = sorm_result.failure_probability
assert abs(probability - result.failure_probability) < 1e-8

SORMOptions(fit="curve"), the default, uses curvature from the Hessian; fit="point" fits boundary points. sorm_result.approximations gives Breitung’s probability ("breitung", the estimate by default) and the Hohenbichler–Rackwitz modification ("modified_breitung"). Here the boundary is a plane, so FORM and SORM agree with the exact probability. For a curved boundary, inspect fitting diagnostics and compare with an independent estimate.

SORM requires standard normal coordinates. A Student-t copula can still be mapped to independent normals through Rosenblatt; explicit spherical Student-t coordinates are a different choice. See Copulas and isoprobabilistic transformations.

Continue: Interpreting results and convergence · Reliability algorithms and results · FORM, SORM and design-point diagnostics