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Failure rate converter
Every unit failure data arrives in, converted at once: FIT, per hour, per million hours, per year and MTTF. Plus what the number means in practice: the chance a device has failed after a number of years, the failures to expect across a fleet, and the λDD / λDU split.
In practice
Split a dangerous failure rate
Treats the value above as λD, all dangerous failures.
| Unit | Value | Note |
|---|
Probability that one device has failed at least once, 1 − e^(−λt). Hover or tap for the date and value, or focus the chart and use the arrow keys.
Constant failure rates only (the flat part of the bathtub curve). First Out includes no licensed failure rate database: take the values from the device certificate, FMEDA report or your own field data, and record the source. Calculations run in your browser; nothing you enter here is sent anywhere.
Method
The conversions
λ per hour = FIT × 10⁻⁹ = (per 10⁶ h) × 10⁻⁶ = (per year) / 8,760 MTTF = 1 / λ (hours; divide by 8,760 for years) P(t) = 1 − e^(−λ · t) probability of at least one failure by time t Fleet = n · λ · 8,760 expected failures per year across n devices λDD = DC · λD λDU = (1 − DC) · λD SFF = (λS + λDD) / (λS + λD)
Worked check
250 FIT = 2.5 × 10⁻⁷ per hour = 2.19 × 10⁻³ per year; MTTF = 4,000,000 hours, about 457 years. Across 200 devices expect about 0.44 failures a year, one every 2.3 years. The chance that one device has failed within 10 years is 2.2 %. With 60 % diagnostic coverage, λDD = 150 FIT and λDU = 100 FIT; with λS = 400 FIT the safe failure fraction is (400 + 150) / 650 = 84.6 %.
Traps
- MTBF is not 1 / λDU. It normally counts every failure; dividing 1 by MTBF gives the total rate.
- MTTF is not a lifetime. An MTTF of 457 years still means about 2 % of devices fail in 10 years, and useful life is a separate limit in the safety manual.
- Per demand is not per hour. Human error and some mechanical data come as a probability per demand or per task.
- Check the unit twice. A factor of 1,000 between FIT and per 10⁶ hours is the most common input error in SIL calculations.
Questions
Short answers; the knowledge library has the long ones.
How do I convert FIT to failures per hour?
One FIT is one failure per 10⁹ device-hours, so multiply by 10⁻⁹. 250 FIT is 2.5 × 10⁻⁷ failures per hour, about 0.0022 failures per year.
Is MTBF the same as 1 / λDU?
No. MTBF normally covers all failures, safe and dangerous, detected and undetected. One divided by MTBF is the total failure rate. A SIL calculation needs λDU and λDD from the FMEDA or certificate.
Does an MTTF of 100 years mean the device lasts 100 years?
No. MTTF describes the constant failure rate period. With an MTTF of 100 years, about 10 % of devices fail within 10 years. Wear-out and useful life are separate limits, given in the safety manual.
How are λDD and λDU found from diagnostic coverage?
λDD is the diagnostic coverage times λD, and λDU is the rest. The safe failure fraction is λS plus λDD, divided by the total failure rate.
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