For reviewers and tool qualification
Validation report
What is tested, against what, and how closely, for every calculation First Out AI and the free calculators perform. With benchmark cases you can repeat in your own spreadsheet, and the evidence you need to qualify the tool under your company's procedure.
Summary
Five independent checks. The engine is written twice, in Python and JavaScript, and each must reproduce the other; both are checked against hand calculations and the published simplified equations.
| Test set | Cases | Compared with | Tolerance | Result, v0.3.0 |
|---|---|---|---|---|
| Reference engine unit tests | 33 | Hand calculations; IEC 61508-6 simplified equations for 1oo2, 2oo3, 1oo3 with common cause, repair and detected failures; imperfect and partial stroke testing | 1 % (1oo1), 3 % (redundant), 2 % (imperfect testing) | All pass |
| Server engine against the reference | 300 random functions, 40 LOPA, 84 worked-example runs | Python reference, same inputs | 10⁻⁹ relative | All pass |
| Independent closed-form check | 26 | Calculations written separately from the engine | 3 % | All pass |
| Free calculators against the server engine | 300 subsystems × 5 values, 200 LOPA, 40 interval searches | Server engine functions | 10⁻¹²; interval searches must meet the target and fail at +1 % | All pass |
| Band limits | 23 boundary values | Defined rule: round to ten significant digits, then compare | Exact | All pass |
Benchmark cases to reproduce
Illustrative inputs, one subsystem each, in failures per hour and hours. Compute them in your own spreadsheet or tool; the simplified values follow the equations on the PFDavg calculator page.
| Case | Voting and inputs | Simplified, perfect test | Time-domain over MT | SIL band |
|---|---|---|---|---|
| B1 | 1oo1 · λDU 2 × 10⁻⁷ · T1 8,760 · MRT 8 · PTC 100 % · MT 20 years | 8.776 × 10⁻⁴ | 8.771 × 10⁻⁴ | SIL 3 |
| B2 | As B1 with PTC 90 % | 8.776 × 10⁻⁴ | 2.538 × 10⁻³ | SIL 2 |
| B3 | 1oo2 · λDU 1 × 10⁻⁶ · β 5 % · T1 8,760 · MRT 8 · MT 20 years | 2.426 × 10⁻⁴ | 2.424 × 10⁻⁴ | SIL 3 |
| B4 | 2oo2 · λDU 3 × 10⁻⁷ · β 5 % · T1 8,760 · MRT 8 · MT 20 years | 2.633 × 10⁻³ | 2.563 × 10⁻³ | SIL 2 |
| B5 | 2oo3 · λDU 5 × 10⁻⁷ · λDD 2 × 10⁻⁶ · β 10 % · βD 5 % · T1 8,760 · MRT 8 · MTTR 24 · MT 20 years | 2.398 × 10⁻⁴ | 2.378 × 10⁻⁴ | SIL 3 |
| B6 | 1oo3 · λDU 1 × 10⁻⁶ · β 2 % · T1 17,520 · MRT 8 · MT 20 years | 1.766 × 10⁻⁴ | 1.766 × 10⁻⁴ | SIL 3 |
| B7 | 1oo2 · λDU 8 × 10⁻⁷ · β 5 % · T1 8,760 · PTC 80 % · MRT 8 · MT 15 years | 1.904 × 10⁻⁴ | 8.592 × 10⁻⁴ | SIL 3 |
| L1 | LOPA · IEF 0.1 /yr · factors 0.3, 0.5, 0.1 · tolerable 10⁻⁵ /yr | MEF 1.5 × 10⁻³ /yr · RRF 150 · PFD required 6.67 × 10⁻³ | SIL 2 | |
| L2 | LOPA · IEF 1 /yr · factors 0.1, 0.1 · tolerable 10⁻⁴ /yr | RRF exactly 100 after rounding to ten significant digits (floating point gives 100.00000000000001) | SIL 1 | |
Expected differences: B2 and B7 show what imperfect proof testing does, which the simplified equations do not model. In B4 the time-domain value is lower because it applies β to the 2oo2 group, where the simplified 2oo2 equation has no common cause term. With 100 % coverage the two values agree within 1 % in the other cases.
Tool qualification
Using First Out AI under your own procedure
IEC 61508-3 asks the organisation that uses a software tool to justify its choice, according to how much the tool's output can affect the safety-related result, and to keep the evidence. IEC 61511 leaves the choice of calculation tools to the user's management of functional safety and verification. Neither requires a certified calculation tool; both require that you can show the tool is fit for the purpose you use it for. Many organisations treat a SIL calculation tool as an off-line support tool whose errors could leave a design fault undetected, and qualify it with a documented validation.
A practical qualification in five steps
- Classify the use. Record what First Out AI is used for (for example, PFDavg and architectural checks in SIL verification reports) and the class your procedure assigns.
- Repeat the benchmarks. Run cases B1 to B7 and L1, L2 above, plus two or three typical functions of your own, in the app and in your existing method. Record the results and the engine version shown in every report.
- Check the methods against your rules. Compare the methods page with your company's calculation standard: averaging horizon, treatment of 2oo2 common cause, Route 1H or IEC 61511 fault tolerance, rounding at band limits.
- Keep the evidence. Store this report, the test set and your comparison with the project or the tool register.
- Recheck on change. The engine version is printed on every report. A new version is listed in the version history on this page with what changed; repeat step 2 for any version you adopt.
What First Out provides
- The published methods, this report and the full test set with inputs and expected results.
- The engine version on every report and export, and a version history with every change that affects a result.
- For Team and Enterprise licences, on request: the test log of the release you use, and notice before a release that changes a result.
Limits
- First Out AI is not certified software and has not been assessed by a third party. Results must be checked by a competent functional safety engineer.
- Failure rates are constant; wear-out is handled through the mission time, not modelled.
- PFH is reported only for 1oo1, 1oo2, 2oo2, 1oo3 and 2oo3; other votings are flagged, not extrapolated.
- The diverse-element rule for systematic capability is not applied.
- AI answers are explanations, not calculations, and are never used in a result.