Analyze Example: AT610 (FORM Only)

This page documents a basic analyze run without SORM or Monte Carlo.

Note: Table values are rounded to 4 significant figures for readability. Very small/large values use scientific notation. Refer to the Excel/JSON result files for full precision. Note: Advanced solver diagnostics (for example lsf_mult and bound multipliers) are included in the Excel/JSON outputs.

Run Context

Problem module:

• problems/AT610Problem.py

Recorded result set:

• results/2026-03-26/13-48-09/AT610-16541.xlsx
• results/2026-03-26/13-48-09/AT610-16541.json
• results/2026-03-26/13-48-09/AT610-16541.py
• results/2026-03-26/13-48-09/AT610-16541.pickle
• results/2026-03-26/13-48-09/AT610-16541.pdf
• results/2026-03-26/13-48-09/profile-16541.yaml

Profile and run mode from saved profile:

• Profile used: default
• run_type: analyze
• include_sorm: false
• include_mc: false
• mc_with_is: false

For results-folder and filename conventions, see CLI Result Files.

Equivalent command shape:

reliafy analyze <profile>

Profile Customization

This example uses the default profile, but analyze behavior is configurable. See Profile Options Reference.

• FORM behavior: reliability_options.form_xtol, form_gtol, form_maxiter, form_random_start.
• Analyze toggles: run_configuration.include_sorm, include_mc, mc_with_is.

Problem File Used

Source: Ang, A. H-S. and Tang, W. H., Probability Concepts in Engineering Planning and Design, Vol. II, Wiley, 1990, p. 368, Problem 6.10.

AT610Problem.py defines:

• Stochastic variables: Y, Z, M
• Distributions: lognormal, lognormal, gumbelmax
• Correlation: corr(Y, Z) = 0.4
• Limit state:
• R = Y * Z
• L = M
• g = R - L

Extracted Results Worksheet Tables

The tables below are transcribed from the Results worksheet in AT610-16541.xlsx.

Header Information

Field	Value
Problem	AT610
Request ID	a3a7191398bd416abb6a3fff41f16541
Run time	00 min 00.33 sec

FORM Results

beta	pf	beta_count	hbeta_count	lsf_count	glsf_count	hlsf_count	nit	min_tries	min_method	lsf_mult
2.6644	0.0038566	5120	4952	7	0	0	10	1	tr_interior_point	0.01110

Stochastic Variable Inputs and FORM Failure Point Outputs

var_name	var_type	mean	std	x	u	alpha	importance
Y	LogNormal	40	5	33.7837	-1.2942	-0.4857	-0.4307
Z	LogNormal	50	2.5	47.7543	-0.4097	-0.1538	-0.1728
M	GumbelMax	1000	200	1613.3165	2.2926	0.8605	0.8858

User-Defined Correlation Inputs

var 1	var 2	cor_x	cor_z
Y	Z	0.4	0.4013

Notes Reported by Reliafy

1. Validation: Stochastic variables definition and limit state function validation required 2 function calls.
2. Validation: Validation of the limit state function's analytic gradient and hessian required 37 function calls.
3. FORM: The lagrange multipliers for the bounds of variable(s) Y, Z and M are active (not zero). If they are large relative to Beta (2.664), try truncating the statistical distribution for these variables and check if the reliability index changes significantly.

Interpretation Snapshot

• This run isolates FORM behavior (no SORM, no Monte Carlo), which is useful for quick reliability screening.
• The reliability index is beta = 2.6644 with pf = 3.8566e-03.
• The failure point importance ranking is dominated by M, then Y, then Z.

Generated Figures

The PDF result file for this run is saved as results/2026-03-26/13-48-09/AT610-16541.pdf.

Figure 1: Importance Factors