RELIABILITY — MONTE CARLO ON A SURROGATE

Trains a surrogate on the dataset, draws Monte Carlo samples from the input space, and reports failure probability and reliability index against a user-supplied limit-state threshold. Cheap because every evaluation hits the surrogate, not the real solver. Use this worker to estimate P_f and beta when running the full solver at every sample would be prohibitive.

When to use

Tagged: beta, design_point, failure_probability, kriging, limit_state, monte_carlo, pf, polynomial.

Inputs

Label	ID	Type	Default	Required	Description
Dataset	dataset	dataset	—	✓	Training dataset (rows of numeric observations) used to fit the surrogate; must contain at least 4 rows and all columns named in independents and clabel.
Input Features	independents	select	—	✓	Multi-select list of numeric input feature column names from the dataset that form the surrogate’s independent variables.
Response Column	clabel	select	—	✓	Single numeric response column from the dataset against which the limit-state threshold is applied.
Surrogate	surrogate_type	select	polynomial_o2		Surrogate model family to train before sampling: polynomial order 1/2/3, Kriging (Gaussian), or Custom (skip training and reuse a saved Lucy ML model); defaults to polynomial_o2.
Saved Surrogate (mfile path or mathmodel id)	surrogate_file	text	—		Only used when surrogate_type=Custom; supply a path to a .pkl mfile or a numeric mathmodel ID pointing to a previously saved Lucy ML model — leave blank for all other surrogate types.
Limit-state Threshold	threshold	text	—	✓	Numeric limit-state value that separates safe from failed designs (e.g. 50.0 for a displacement limit in mm); no default — must be supplied.
Failure Direction	direction	select	greater		Defines which side of the threshold constitutes failure: ‘greater’ (response > threshold) or ‘less’ (response < threshold); defaults to greater.
Sample Count	n_samples	text	10000		Number of Monte Carlo draws; 10 000 gives ~1% standard error at P_f = 0.01, raise to 100 000 for rare-event accuracy; clamped to [100, 1 000 000], defaults to 10 000.
Input Distribution	distribution	select	uniform		Marginal distribution used to draw each input: ‘uniform’ samples uniformly between the training-data min/max per column; ‘normal’ samples from the per-column mean and standard deviation; defaults to uniform.
Random Seed	seed	text	—		Optional integer seed for reproducible runs. Leave blank for non-deterministic.

Outputs

Label	ID	Type	Description
Failure Probability	failure_probability	scalar	Estimated failure probability P_f in [0, 1]: fraction of Monte Carlo samples whose surrogate response violates the limit state.
Reliability Index (beta)	reliability_index_beta	scalar	Reliability index β = −Φ⁻¹(P_f); higher values indicate greater reliability (β ≈ 3 corresponds to P_f ≈ 0.0013).
Failure Count	n_failures	scalar	Integer count of Monte Carlo samples classified as failed (response violated the limit-state direction).
Sample Count	n_samples	scalar	Integer echo of the actual number of Monte Carlo samples evaluated (after clamping to [100, 1 000 000]).
Design Point	design_point	json	JSON object representing the single Monte Carlo sample whose predicted response is closest to the limit-state threshold — the approximate most-probable point of failure.
Monte Carlo Samples	samples	dataset	Dataset containing all Monte Carlo samples augmented with the surrogate-predicted response value and a boolean ‘failed’ flag for each row.
Reliability Summary	reliability_summary	json	JSON blob capturing the full run configuration (surrogate type, threshold, direction, distribution, seed) alongside all computed metrics (P_f, β, n_failures) for audit and reporting.

Disciplines

• ai_ml.surrogate
• design_exploration.reliability

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