Weibull Analysis Calculator
Weibull analysis turns a set of failure times into a model of how a population fails over time. It is the default life-data distribution in reliability engineering because a single shape parameter, β (beta), distinguishes infant mortality from random failure from wear-out — which tells you whether to fix the process, the design, or the maintenance interval.
Formula
Worked example
A pump seal fleet is fitted to a 2-parameter Weibull with β = 2.1 and η = 1200 operating hours.
- β = 2.1 is greater than 1, so the hazard rate is increasing — this is wear-out, not random failure.
- R(500) = exp[−(500/1200)^2.1] = exp[−0.1590] = 0.853
- B10 = 1200 × (0.10536)^(1/2.1) = 1200 × 0.3424 = 411 hours
- MTTF = 1200 × Γ(1 + 1/2.1) = 1200 × 0.8857 = 1063 hours
85.3% of seals survive to 500 hours, 10% have failed by 411 hours, and mean life is 1063 hours. Because β > 1, a scheduled replacement interval is justified — for a random-failure item (β = 1) it would not be.
How to interpret the result
| β < 1 | Decreasing hazard — infant mortality. Look at manufacturing defects, installation error, burn-in. |
| β ≈ 1 | Constant hazard — random failure. Scheduled replacement does not help; condition monitoring might. |
| 1 < β < 4 | Increasing hazard — classic wear-out. Preventive replacement intervals become cost-effective. |
| β > 4 | Steep wear-out, often fatigue or corrosion with a well-defined life limit. |
Common mistakes
- Treating suspensions (units still running) as failures. Censored data must be entered as suspensions or β and η will both be biased low.
- Fitting a Weibull to a mixture of failure modes. Two mechanisms produce a curved probability plot — split the data by mode and fit each separately.
- Reporting MTTF as though it were a typical life. For β > 1 the mean sits well above the median; B10 or B50 communicates far better to a maintenance planner.
- Fitting with fewer than about 7 failures without confidence bounds. Small samples give deceptively tidy point estimates.
Frequently asked questions
- What is a good beta value in Weibull analysis?
- There is no universally good value — beta describes behaviour, not quality. β below 1 points to infant mortality, β near 1 to random failure, and β above 1 to wear-out. What matters is whether the beta you measured matches the failure mode you assumed.
- What is the difference between eta and MTBF?
- Eta (η) is the characteristic life: the time by which 63.2% of the population has failed, regardless of beta. MTBF is a mean. They are equal only when β = 1. Using them interchangeably is one of the most common errors in reliability reporting.
- How many failures do I need for a Weibull fit?
- Useful estimates start around 5–7 failures, but always report confidence bounds below roughly 20. With very few failures, a Weibayes analysis with an assumed beta from similar hardware is often more defensible than a free fit.
Related tools
About Reliability Pro
Weibull Solver is part of a suite of 126 reliability, maintenance and quality engineering tools covering life data analysis, accelerated testing, system reliability, FMEA and root cause, SPC, and design for reliability. It runs in the browser and as native iOS and Android apps, so the same calculation is available at a desk or in front of the asset.