Advanced Analysis
Weibull Analysis Calculator
Reliability, hazard rate, B-life, and mean life from the Weibull shape (β) and scale (η) parameters — and what β says about how a component fails.
R(t) = e^(−(t/η)^β)β < 1: infant mortality | β = 1: random | β > 1: wear-out
Time at which 63.2% of units have failed
What is Weibull analysis?
The Weibull distribution is the most widely used distribution in reliability engineering. Unlike the simpler exponential distribution (constant failure rate), Weibull can model increasing, decreasing, or constant failure rates — making it suitable for real-world components.
R(t) = e^(−(t / η)^β)β (shape) sets how the failure rate changes with age; η (scale, characteristic life) is the time by which 63.2% of units have failed.
Shape parameter (β) interpretation
| β | Failure pattern | What to do |
|---|---|---|
| β < 1 | Infant mortality — failure rate decreases over time | Screen out early failures with burn-in testing |
| β = 1 | Random failures — constant failure rate (reduces to exponential) | Time-based replacement will not help |
| β > 1 | Wear-out — failure rate increases | Schedule preventive replacement before B10 life |
| β ≈ 3.5 | Approximates the normal distribution | — |
Typical β values by component
| Component | β range | Failure mode |
|---|---|---|
| Electronics (ICs) | 0.5 – 1.0 | Infant mortality → random |
| Bearings | 1.5 – 2.5 | Fatigue wear-out |
| Belts / seals | 2.0 – 3.0 | Degradation wear-out |
| Gears | 2.0 – 5.0 | Tooth fatigue |
| Corrosion | 3.0 – 6.0 | Progressive degradation |
Typical ranges for orientation only — fit β to your own failure data before acting on it.