PFDavg and SIL Calculator
Estimate the average probability of failure on demand (PFDavg) of a safety function element from its dangerous undetected failure rate and proof test interval, for common voting architectures.
- TI = 12 months = 8,760 h, λDU = 2.00 × 10^−6 /h
- PFDavg = λDU × TI ÷ 2 = 0.00876
SIL bands for low demand mode (IEC 61508 and 61511)
| SIL | PFDavg | Risk reduction |
|---|---|---|
| SIL 4 | 10⁻⁵ to 10⁻⁴ | 10,000 to 100,000 |
| SIL 3 | 10⁻⁴ to 10⁻³ | 1,000 to 10,000 |
| SIL 2 | 10⁻³ to 10⁻² | 100 to 1,000 |
| SIL 1 | 10⁻² to 10⁻¹ | 10 to 100 |
Simplified PFDavg Equations
1oo2: (λDU TI)² ÷ 3 + β λDU TI ÷ 2
2oo2: λDU × TI
2oo3: (λDU TI)² + β λDU TI ÷ 2
λDU is the dangerous undetected failure rate of one channel, TI the proof test interval and β the fraction of failures due to common cause. 1 FIT = 1 failure per 10⁹ hours.
Worked example
A valve assembly with λDU = 2000 FIT, tested yearly (8760 h): 1oo1 PFDavg = 2 × 10⁻⁶ × 8760 ÷ 2 = 8.76 × 10⁻³, which is SIL 2. Two valves in 1oo2 with β = 10 % give about 9.8 × 10⁻⁴, SIL 3 by PFD.
Frequently Asked Questions
What is PFDavg?
The average probability that a safety function fails to act when demanded, over the proof test interval.
How does the proof test interval affect SIL?
For 1oo1, PFDavg is proportional to the test interval: testing twice as often halves the PFDavg.
Is PFDavg enough to claim a SIL?
No. You must also meet architectural constraints (hardware fault tolerance), systematic capability and the safety lifecycle requirements of IEC 61511.
Learn more on the blog
What is SIL (safety integrity level)
A practical, field focused guide on instrumentationblog.in that explains the theory behind this calculator and how engineers apply it on real plants.
Read Full Article