What the calculator is for
Failure data arrive in different units. A certificate or FMEDA states λDU in FIT, a reliability database in failures per 10⁶ hours, a maintenance system as failures per year, and a vendor brochure as MTBF. SIL verification, PFDavg and spurious-trip estimates all need the same quantity: a failure rate per hour. This converter puts every form side by side, so you can check a datasheet value or move a number between documents without a slip in the powers of ten.
- FIT (failures in time) is failures per 10⁹ device-hours: 1 FIT = 10⁻⁹ per hour.
- Failures per year = λ × 8,760 h.
- MTBF = 1 / λ for a constant failure rate. For non-repairable items the same figure is called MTTF.
Worked example
A pressure transmitter certificate gives λDU = 250 FIT. That is 2.5 × 10⁻⁷ per hour, or 0.00219 dangerous undetected failures per device-year. The MTBF for that failure mode is 1 / 2.5 × 10⁻⁷ = 4 × 10⁶ h, about 457 years.
That does not mean the transmitter lasts 457 years. With 1,000 such transmitters on a site you should expect about 2.2 dangerous undetected failures every year. For a single channel proof tested once a year, PFDavg ≈ λDU × T / 2 = 1.1 × 10⁻³: try it in the PFD calculator.
Quick reference
| FIT | Per hour | Per year | MTBF (years) |
|---|---|---|---|
| 10 | 1 × 10⁻⁸ | 8.76 × 10⁻⁵ | 11,400 |
| 50 | 5 × 10⁻⁸ | 4.38 × 10⁻⁴ | 2,280 |
| 100 | 1 × 10⁻⁷ | 8.76 × 10⁻⁴ | 1,140 |
| 250 | 2.5 × 10⁻⁷ | 0.00219 | 457 |
| 500 | 5 × 10⁻⁷ | 0.00438 | 228 |
| 1,000 | 1 × 10⁻⁶ | 0.00876 | 114 |
| 5,000 | 5 × 10⁻⁶ | 0.0438 | 22.8 |
Common mistakes
- Reading MTBF as a lifetime. It is the reciprocal of a rate during the useful-life period, not the age at which a device wears out.
- Mixing failure modes. A total λ, λD and λDU differ by an order of magnitude or more. Convert the mode your calculation needs.
- Per 10⁶ hours versus FIT. 1 failure per 10⁶ h is 1,000 FIT, not 1 FIT.
- Hours per year. 8,760 h is usual. 8,766 h (365.25 days) changes the result by less than 0.1 %, so set it under Advanced only to match another document.
Basis
The conversion assumes a constant failure rate (the flat part of the bathtub curve), as IEC 61508-6 and IEC 61511 do for random hardware failures. The probability of at least one failure within time t is 1 − e−λt. Failure rates quoted at reference conditions (IEC 61709, SN 29500) still need adjusting for your temperature and stress.