Advanced SIL Verification Calculator (1oo2 Example)
This calculator illustrates a more realistic approach to SIL verification for a 1oo2 SIF (one-out-of-two) architecture, considering factors like common cause (β), diagnostic coverage (DC), proof test intervals, and partial stroke testing. Actual formulas can be significantly more complex, but this provides a taste of how real-world scenarios go beyond the simple 1oo1 calculation.
- 1oo2 Voting: At least one channel must function to avoid failure. Redundancy improves availability but adds complexity.
- Common Cause (β): A fraction of failures can simultaneously affect both channels (e.g., design flaws, environmental events).
- Diagnostic Coverage (DC): Automated diagnostics can detect certain failures, reducing the probability of undetected dangerous failures.
- Partial Stroke Tests: Intermittent partial checks can reduce the average time a dangerous failure goes undetected, improving PFD.
Enter Parameters
Failure rates (λD) are “dangerous undetected” rates (in failures per hour). Proof test intervals in hours (e.g., 8760 hrs ≈ 1 year).
| SIL | PFD Range (Avg) |
|---|---|
| SIL 1 | 1e-2 to 1e-1 |
| SIL 2 | 1e-3 to 1e-2 |
| SIL 3 | 1e-4 to 1e-3 |
| SIL 4 | 1e-5 to 1e-4 |
Compare your calculated PFDavg to these SIL ranges for approximate classification. Actual criteria may also include architectural constraints, systematic capability, etc.
Illustrative Formulas Used
The approximate formula for each channel’s undetected dangerous failure rate is:
- Effective λDU = λD × (1 − DC/100)
- Then, the average PFD is roughly λDU × (Tavg), but we break it down with partial stroke intervals, etc.
For 1oo2, the probability of failing to danger is more complex. We consider independent failures plus a fraction for common cause (β). The simplified approach here is:
- PFD(1oo2) = PFD(A fails AND B fails) + Common cause fraction.
- We incorporate partial stroke coverage by reducing the effective interval for a portion of the failures.
Again, this is a simplified illustration. Real tools may combine exponential models, separate phases, Markov chains, or reliability block diagrams to handle partial coverage, mission times, and multi-phase repairs.
Disclaimer:
- This is an illustrative calculator, not an authoritative design tool.
- Real SIL verification often requires specialized software, vendor reliability data, mission times, partial stroke test coverage, systematic failure analyses, and thorough documentation.
- Use this code as an educational example of more advanced parameters, not a final design solution.
Explanation of This Example
- 1oo2 Voting: A SIF uses two channels (A and B). The system fails only if both channels fail simultaneously (assuming no common cause).
- Diagnostic Coverage (DC): If your sensor, logic solver, or final element has internal diagnostics, some fraction of dangerous failures are caught before demand. Effective failure rate is λD×(1−DC)\lambda_{D} \times (1 – DC)λD×(1−DC).
- Common Cause (β): A percentage of failures that simultaneously affect both channels, bypassing the benefit of redundancy.
- Partial Stroke Testing: With partial tests at interval TpT_pTp that detect a fraction coverage=Cvp\text{coverage} = Cvpcoverage=Cvp of dangerous failures early, the average time a failure can remain hidden is reduced. Meanwhile, the rest of failures are only discovered during the full test at interval TTT.
- Overall PFD: This snippet shows a simplified formula that sums the probability that both channels fail independently plus a portion due to common cause.
Conclusion
This advanced “real-world” SIL verification calculator example introduces some typical complexities:
- Redundancy (1oo2 architecture)
- Common cause fraction
- Diagnostic coverage
- Partial stroke tests
Even so, real functional safety analyses (per IEC 61508 or IEC 61511) typically require more nuanced reliability block diagrams, vendor data, mission time constraints, and additional constraints for systematic failures. Use this snippet for educational or illustrative purposes, and always consult a functional safety specialist or official tools for production-level SIL verification.