Troubleshooting reliability analyses

FORM does not converge

Read FORMResult.message, iterations, limit_state_error and direction_error. Check the limit-state sign, units and values near the trial point. Nonfinite values, a zero gradient or a discontinuity require attention to the response model or method choice. Verify analytical derivatives against finite differences. Review starting points and tolerances before increasing the iteration budget. See Running FORM and SORM and Direct differentiation of the limit state.

FORM converges but methods disagree

Convergence describes the design-point iteration. Curvature, competing failure regions and transformation ordering can change the approximation error. Inspect the physical design point, compare an independent simulation, and use Strong Maximum Test where applicable. The test can miss bounded failure islands, so an empty set of competing points is not a global guarantee.

Monte Carlo observes zero failures

Do not interpret a zero count as proof that failure is impossible. For a preselected, fixed sample size of N independent direct trials with no failures, a one-sided 95 % binomial upper confidence limit is \(1-0.05^{1/N}\) (approximately \(3/N\)). This formula does not apply unchanged to importance weights, correlated subset chains or adaptive stopping. Increase the budget or choose a rare-event estimator using Choosing a reliability method.

A probability is zero but the reliability index is finite

The probability has underflowed: it is below the double range, about \(5 \times 10^{-324}\), or it underflowed in an intermediate step. SORM, importance sampling and line sampling compute the reliability index from its logarithm, so report the index. See Working at high reliability.

Evaluation stops at nonfinite physical points

AnalysisError with “requires finite physical points” means that a point passed to the limit state contained NaN or infinity. Possible causes are nonfinite inputs, overflow in a custom transformation, and a custom distribution that overrides cdf or ppf without sf and isf. Built-in distributions with unbounded tails stay finite to \(|u| \approx 37.5\). A bounded support is a different matter: its points stay finite but reach the bound itself, where they can no longer be inverted. See Working at high reliability.

Sampling estimates change between runs

Record seeds, budgets and achieved precision, then repeat independent runs. For subset simulation, inspect intermediate thresholds and chain behavior; the reported cov neglects chain correlation. For surrogate methods, separate training variability, surrogate bias and final sampling variability. See Estimating failure probability by simulation and Active-learning methods and literature.

A transformation is unsupported

Check the copula, variable order and chosen standard space together. A Student-t copula does not require Student-t standard coordinates. Rosenblatt maps supported continuous joint laws to independent standard normals, which are required by several classical algorithms. Explicit spherical Student-t coordinates have different algorithm support. See Copulas and isoprobabilistic transformations.

Active learning stops at its budget

Inspect the stopping reason and convergence record; reaching the evaluation limit is not evidence that the surrogate meets the convergence criterion. Reserve independent evaluations for validation. Review the learning function, surrogate fit and estimator coverage in Active-learning methods and literature.

A notebook cannot import an object

Confirm the notebook kernel uses the environment where the development version is installed. Inspect sys.executable, pystra.__version__ and pystra.__file__ inside that kernel. Install the al extra for the active-learning tutorials and retain any helper files in the runnable bundle. See Installation and Migrating from 1.x to 2.0 for environment and API changes.

Continue: Choosing a reliability method · Interpreting results and convergence · Reliability algorithms and results