Analyze Example: Chan3 (SORM + Monte Carlo)

This page documents an analyze run with both SORM and Monte Carlo enabled (-s -m).

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.

Run Context

Problem module:

problems/Chan3Problem.py

Recorded result set:

results/2026-03-26/13-49-14/Chan3-55cde.xlsx
results/2026-03-26/13-49-14/Chan3-55cde.json
results/2026-03-26/13-49-14/Chan3-55cde.py
results/2026-03-26/13-49-14/Chan3-55cde.pickle
results/2026-03-26/13-49-14/Chan3-55cde.pdf
results/2026-03-26/13-49-14/profile-55cde.yaml

Profile and run mode from saved profile:

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

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

Equivalent command shape:

reliafy analyze <profile> -s -m

Option meaning in this command:

-s enables SORM (second-order reliability analysis).
-m enables Monte Carlo simulation.

Profile Customization

This example uses the default profile, but these options are configurable. See Profile Options Reference.

SORM behavior: reliability_options.sor_method, sor_approximation, sor_fit_method, sor_fdm.
Monte Carlo behavior: reliability_options.mc_n, mc_max_cv, mc_seed, mc_remove_oob.
Analyze toggles: run_configuration.include_sorm, include_mc, mc_with_is.

Problem File Used

Source: Chan, C. L. and Low, B. K., "Practical second-order reliability analysis applied to foundation engineering," International Journal for Numerical and Analytical Methods in Geomechanics, first published: 05 July 2011. →

Chan3Problem.py defines:

Deterministic variables: d, L, a
Stochastic variables: Qv, cp, cs (all Beta)
Correlation: corr(cp, cs) = 0.5
Limit state: g = Resistance - Load

Extracted Results Worksheet Tables

The tables below are transcribed from the Results worksheet in Chan3-55cde.xlsx.

Header Information

Field	Value
Problem	`Chan3`
Request ID	`501c48c8d22c48228352ac5b39855cde`
Run time	`00 min 00.53 sec`

Deterministic Variables

var_name	value
d	0.5
L	10
a	1

FORM Results

beta	pf	beta_count	hbeta_count	lsf_count	glsf_count	hlsf_count	nit	min_tries	min_method	lsf_mult
0.9543	0.1700	5127	4959	7	0	0	11	1	tr_interior_point	0.03079

SORM Results

beta	pf	minR	Ravg	maxR	minabsR	Ks	lsf_class	sor_method	sor_approx	sor_fit_meth	fit_radius	lsf_count
1.1671	0.1216	2.6167	3.9465	8.0246	2.6167	0.5068	Convex ellipsoid	SOSPA_H	Paraboloid	Kiureghian	1	20

Monte Carlo Results

beta	pf	cv	max_cv	size	%_removed	cycles	auto_size	mc_with_is
1.1593	0.1232	0.02436	0.05	12000	0	3	True	False

Stochastic Variable Inputs and FORM Failure Point Outputs

var_name	var_type	mean	std	x	u	alpha	importance
Qv	Beta	360	54	400.7793	0.6283	0.6585	0.6895
cp	Beta	35	5.25	31.7663	-0.4540	-0.4757	-0.1318
cs	Beta	25	3.75	21.9407	-0.5565	-0.5832	-0.7122

Notes Reported by Reliafy

Validation: Stochastic variables definition and limit state function validation required 22 function calls.
Validation: SORM reliability_options.sor_fit_method was changed from None to Kiureghian because sor_approximation is Paraboloid and the selected reliability options require a compatible fit method.
Validation: Validation of the limit state function's analytic gradient and hessian required 4 function calls.
FORM: The lagrange multipliers for the bounds of variable(s) Qv, cp and cs are active (not zero). If they are large relative to Beta (0.954), try truncating the statistical distribution for these variables and check if the reliability index changes significantly.
Monte Carlo: Completed 3 cycles with 4.00e+03 samples per cycle.

Interpretation Snapshot

FORM gives beta = 0.9543 (pf ≈ 0.1700), while SORM and Monte Carlo indicate a slightly less severe reliability level (beta ≈ 1.16).
SORM and Monte Carlo are closely aligned (pf ≈ 0.1216 vs 0.1232), which supports consistency of the higher-order/empirical estimate.
Monte Carlo precision is acceptable for this run (cv = 0.02436 < 0.05).