Core Reliability
Failure Rate Calculator (λ)
Failure rate (lambda) from MTBF or from operating data, with step-by-step working and FIT conversion.
λ = n ÷ T = 1 ÷ MTBFWhat is failure rate?
Failure rate (λ, lambda) is the frequency with which a system or component fails, expressed in failures per unit of time. It is the reciprocal of MTBF and is fundamental to reliability engineering.
- Predicts the expected number of failures over time
- Used in reliability calculations, R(t) = e^(−λt)
- Enables spare parts planning
- Drives warranty cost estimation
- Benchmarks against industry standards
Failure rate formulas
From operating data
λ = Number of failures ÷ Total operating timeFrom MTBF
λ = 1 ÷ MTBFLower failure rates indicate more reliable systems. A failure rate of 0.001/hour means one failure expected every 1,000 hours.
Failure rate calculation example
A facility operates 20 identical pumps continuously for one year and records 8 failures:
| Given | Value |
|---|---|
| Number of pumps | 20 |
| Operating hours per pump | 8,760 (24/7) |
| Total failures | 8 |
Total operating time
20 × 8,760 = 175,200 hoursFailure rate
λ = 8 ÷ 175,200 = 4.566 × 10⁻⁵ failures/hourMTBF
1 ÷ λ = 21,900 hoursFIT rate & unit conversions
FIT (Failures In Time)
1 FIT = 1 failure per 10⁹ device-hours| Unit | λ = 0.001/h | Meaning |
|---|---|---|
| Per hour | 0.001 | 1 failure every 1,000 hours |
| Per day | 0.024 | ~1 failure every 42 days |
| Per year | 8.76 | ~9 failures per year |
| FIT | 1,000,000 | 1 million FIT |
Frequently asked questions
What is the difference between failure rate and MTBF?
Failure rate (λ) and MTBF are reciprocals: λ = 1/MTBF. Failure rate expresses how often failures occur (e.g., 0.001 failures/hour), while MTBF expresses the average time between failures (e.g., 1,000 hours). They convey the same information in different ways.
Is failure rate constant over time?
Only during the useful-life period of the bathtub curve. Early life has a decreasing failure rate (infant mortality), and wear-out has an increasing failure rate. A constant failure rate applies during normal operation and follows the exponential distribution.
What is a FIT rate?
FIT (Failures In Time) equals one failure per billion device-hours. It is commonly used in semiconductor and electronics reliability. To convert: FIT = λ (per hour) × 10⁹.
How do I calculate system failure rate from component failure rates?
For components in series (all must work), add the individual failure rates: λ_system = λ₁ + λ₂ + … + λₙ. For parallel systems with redundancy the calculation is more complex — use the System Reliability calculator.