.. _auto_reliability_mc:

*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
------

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   :widths: 20 20 20 20 20 20

   * - 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
-------

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   :header-rows: 1
   :widths: 20 20 20 20

   * - 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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   Auto-generated from <code>platform</code> schema. Worker id: <code>reliability_mc</code>. Schema hash: <code>2d903ef006cf</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
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