Interpreting results and convergence

Report the event, probability model, method, convergence status and numerical precision together. A failure probability without its reference period or modeling assumptions is incomplete.

Result records

Every analysis’s run() returns an immutable record from pystra.results. Its values remain a snapshot if the analysis is rerun, and its vector fields are read-only arrays in variable_names order.

Fields common to every record

Field	Meaning
status, message, converged	How the method terminated. converged is true for the statuses "converged" and "completed".
failure_probability, beta	The estimate and its normal-equivalent index, \(-\Phi^{-1}(p_f)\). Diagnostic records (Strong Maximum Test, distribution analysis) have neither.
n_limit_state_evaluations	Limit-state evaluations made by this run. Active-learning results and their history steps count true-model calls under the same name.
method, variable_names	The analysis, and the order of the vector fields.

summary() returns a short plain-text report.

Status values

status	Meaning
"converged"	A design-point method (FORM, SORM, system FORM, sensitivity) met its convergence criteria.
"not_converged"	It did not, or SORM’s formula is undefined at the fitted curvatures. There is no estimate. The analysis raises AnalysisError, which carries this record, unless constructed with on_failure="return".
"completed"	A simulation or diagnostic ran to completion.
"precision_not_met"	A simulation used its sample budget before reaching its target coefficient of variation. The estimate is reported, with its coefficient of variation.

FORM records

FORMResult adds:

Field	Meaning
design_point_x	The design point in physical coordinates and original units.
design_point_u, standard_space	The same point in the chosen standard coordinates.
alpha	The unit direction from the origin towards the design point.
design_index	Signed distance of the design point; equals beta in normal space.
iterations, limit_state_error, direction_error	Diagnostics for the iteration and its termination.

to_dataframe() tabulates the design point and alpha by variable. An unconverged record has no probability, reliability index or design point. The record’s beta is normal-equivalent. This distinction matters for explicit spherical Student-t transformations; see Notation and probability spaces.

Other records

Record	Returned by, and what it adds
SORMResult	SORM: form, fit, curvatures, formula and approximations, the Breitung and modified Breitung probabilities.
SimulationResult	Crude Monte Carlo, importance, line and subset sampling: coefficient_of_variation, n_samples and method-specific diagnostics.
SystemFORMResult	System FORM: bounds, component_results, correlation and intersections.
SensitivityResult	Sensitivity analysis: marginal derivatives and, for the closed form, correlation derivatives, with to_dataframe().
StrongMaximumResult	Strong Maximum Test: a diagnostic, not a probability, with the sample points by region.
DistributionAnalysisResult	Distribution analysis: the samples and their limit-state values.

Calibration and active-learning analyses have their own records. Retain their convergence and termination information when exporting tables.

Separate three sources of error

• Numerical convergence: did the iteration or fit meet its criteria?

• Approximation error: does a tangent plane, quadratic surface or surrogate represent the important failure regions?

• Sampling uncertainty: how variable is an estimate based on finite samples?

A confidence interval on a frozen surrogate’s Monte Carlo estimate addresses the last item, conditional on that surrogate. It does not measure its bias. A completed calculation or a small coefficient of variation does not establish the physical model’s adequacy.

Continue: Troubleshooting reliability analyses · Reliability figures · A first reliability analysis · Reliability algorithms and results