Inverse FORM Examples
This page documents two inverse reliability design examples based on saved design runs.
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 bsr_mult and bnds_mult Lagrange multipliers) are included in the Excel/JSON result files and are not shown in the tables below.
Inverse SORM: Pass --use-sorm (or -s) to the design command to switch the solution algorithm from Inverse FORM to Inverse SORM. All examples on this page were run without this flag (Inverse FORM). The problem file structure is identical for both methods.
Plot Behavior For design Runs
Reliafy does not generate plots as part of design runs (including Inverse FORM).
This keeps outputs manageable when multiple design cases are included in one run.
If you need plots, use the resulting design parameters in a follow-up analyze or simulate run and enable plot/report options there.
In the Excel Results sheet, these details appear under each case as Design point stochastic variables result: and, when available, Load and resistance partial factors:.
Profile Customization
These inverse FORM examples use the default profile, but solver behavior is configurable. See Profile Options Reference.
- Inverse/design solver controls:
reliability_options.design_xtol,design_gtol,design_maxiter,design_random_start. - FORM controls used inside inverse iterations:
reliability_options.form_xtol,form_gtol,form_maxiter,alpha_direction. - Correlation handling and derivative checks:
reliability_options.use_nearest_correlation,check_lsf_diffs_wrtx,check_lsf_diffs_wrtu.
Example A: AT625Problem.py (Single Default Case)
Run Context
Problem module:
problems/AT625Problem.py
Recorded result set:
results/2026-03-15/15-01-56/Ang and Tang 6.25-88679.xlsxresults/2026-03-15/15-01-56/Ang and Tang 6.25-88679.jsonresults/2026-03-15/15-01-56/Ang and Tang 6.25-88679.pyresults/2026-03-15/15-01-56/profile-88679.yaml
Profile and run mode from saved profile:
- Profile used:
default run_type: designinclude_sorm: falseinclude_mc: false
For results-folder and filename conventions, see CLI Result Files.
Equivalent command shape:
reliafy design <profile>
Problem File Used
Source: Ang, A. H-S. and Tang, W. H., Probability Concepts in Engineering Planning and Design, Vol. II, Wiley, 1990, p. 431, Problem 6.25.
Extracted Results Worksheet Tables
Run summary:
| Field | Value |
|---|---|
| Request ID | e580592237a84a2ca36275f5bbd88679 |
| Target beta | 1.28 |
| Target pf | 0.1003 |
| Cases | default |
Default-case inverse FORM result:
| case | beta | pf | lsf_count | glsf_count | hlsf_count | nit |
|---|---|---|---|---|---|---|
| default | 1.28 | 0.1003 | 8 | 8 | 8 | 12 |
Design point stochastic variables result (default):
| var_name | x | fractile | char_value | partial_factor |
|---|---|---|---|---|
| f | 2.52 | 0.5 | 2.46 | 1.024 |
| N | 10.31 | 0.5 | 11 | 0.9374 |
| Y | 9.6 | 0.5 | 9.76 | 0.9836 |
| Q | 1.268e+04 | 0.5 | 9589 | 1.322 |
Load and resistance partial factors (default):
| Load | Resistance |
|---|---|
| 1.322 | 0.9109 |
Notes:
- This is the canonical single-case inverse FORM setup.
AT625also reports load and resistance partial factors in the design output.
Example B: AT624Problem.py (Multi-Case)
Run Context
Problem module:
problems/AT624Problem.py
Recorded result set:
results/2026-03-15/15-01-29/Ang and Tang 6.24-9e10e.xlsxresults/2026-03-15/15-01-29/Ang and Tang 6.24-9e10e.jsonresults/2026-03-15/15-01-29/Ang and Tang 6.24-9e10e.pyresults/2026-03-15/15-01-29/profile-9e10e.yaml
Profile and run mode from saved profile:
- Profile used:
default run_type: designinclude_sorm: falseinclude_mc: false
For results-folder and filename conventions, see CLI Result Files.
Equivalent command shape:
reliafy design <profile>
Problem File Used
Source: Ang, A. H-S. and Tang, W. H., Probability Concepts in Engineering Planning and Design, Vol. II, Wiley, 1990, p. 428, Problem 6.24.
Extracted Results Worksheet Tables
Run summary:
| Field | Value |
|---|---|
| Request ID | 0a4040de1dc341adb06688f5cdd9e10e |
| Target beta | 2.0 |
| Target pf | 0.02275 |
| Cases | 1, 2, 3, 4 |
Case-by-case inverse FORM results:
| case | beta | pf | lsf_count | glsf_count | hlsf_count | nit |
|---|---|---|---|---|---|---|
| 1 | 2.0 | 0.02275 | 7 | 7 | 7 | 10 |
| 2 | 2.0 | 0.02275 | 6 | 7 | 7 | 10 |
| 3 | 2.0 | 0.02275 | 7 | 7 | 7 | 10 |
| 4 | 2.0 | 0.02275 | 7 | 7 | 7 | 10 |
Design point stochastic variables result (all cases):
| case | var_name | x | fractile | char_value | partial_factor |
|---|---|---|---|---|---|
| 1 | N | 1.07 | 0.5 | 1 | 1.07 |
| 1 | M | 0.01259 | 0.5 | 0.01 | 1.259 |
| 1 | Y | 172.3 | 0.5 | 126 | 1.367 |
| 2 | N | 1.07 | 0.5 | 1 | 1.07 |
| 2 | M | 0.06278 | 0.5 | 0.05 | 1.256 |
| 2 | Y | 35.35 | 0.5 | 25.8 | 1.37 |
| 3 | N | 1.071 | 0.5 | 1 | 1.071 |
| 3 | M | 0.1252 | 0.5 | 0.1 | 1.252 |
| 3 | Y | 18.26 | 0.5 | 13.3 | 1.373 |
| 4 | N | 1.075 | 0.5 | 1 | 1.075 |
| 4 | M | 0.6145 | 0.5 | 0.5 | 1.229 |
| 4 | Y | 4.477 | 0.5 | 3.22 | 1.39 |
Load and resistance partial factors:
- No dedicated "Load and resistance partial factors" table was written in this
AT624results workbook, becauseLSFreturnsLandR = Falseand therefore no load/resistance partial factors were calculated or reported.
Notes:
- This example demonstrates the
DesignProblem.casesstructure for running multiple reliability design scenarios in one command. - All cases converge close to the same target reliability while using different case-level input statistics.
Recommended Authoring Pattern
- Start with a single-case definition (
default) to validate setup and derivatives. - Add
caseswhen you need scenario sweeps under a common target reliability. - Keep one summary table per run, then add per-case details (partial factors, design points, failure-point statistics) as needed.