Calculate Weibull reliability with shape (β) and scale (η) parameters. Determine failure probability, reliability, and hazard rate at any time.
The Weibull distribution is the most versatile reliability model in engineering. By adjusting its shape parameter (β, beta) and scale parameter (η, eta), it can model infant mortality (β < 1), random failures (β = 1, equivalent to exponential), and wear-out failures (β > 1).
Weibull analysis is used extensively for life data analysis: predicting product lifetime, planning warranty periods, scheduling preventive maintenance, and conducting accelerated life testing. The B-life concept (e.g., B10 = the time at which 10% of units have failed) is directly calculated from Weibull parameters.
This calculator takes the shape and scale parameters and computes the cumulative failure probability F(t), reliability R(t), hazard rate h(t), and B-life at any specified time t.
This measurement forms a critical foundation for capacity planning, helping teams align production capabilities with demand forecasts and strategic business objectives throughout the planning cycle. Integrating this calculation into regular operational reviews ensures that key decisions are grounded in current data rather than outdated assumptions or rough approximations from the past.
Weibull analysis models the full range of failure behaviors with just two parameters. It handles infant mortality, random failures, and wear-out in a single framework, making it the go-to model for lifecycle reliability engineering. Having accurate figures readily available streamlines reporting, audit preparation, and strategic planning discussions with management and key stakeholders across the business.
F(t) = 1 − e^(−(t/η)^β) R(t) = e^(−(t/η)^β) h(t) = (β/η) × (t/η)^(β−1) B-life: t_B = η × (−ln(1 − B/100))^(1/β) where β = shape, η = scale (characteristic life)
Result: R(2000) = 87.7%, B10 = 2,085 hours
With β = 2.5 (wear-out pattern) and η = 5,000 hours: R(2000) = e^(−(2000/5000)^2.5) = 87.7%. B10 = 5000 × (−ln(0.90))^(1/2.5) = 2,085 hours — 10% of units fail by 2,085 hours.
The bathtub curve is modeled by combining three Weibull distributions: β < 1 for infant mortality, β ≈ 1 for useful life, and β > 1 for wear-out. This composite Weibull model captures the full product lifecycle.
Accelerated life testing (ALT) uses elevated stress to induce failures faster. Weibull analysis of ALT data, combined with acceleration models, allows prediction of reliability at normal use conditions from short test durations.
The standard two-parameter Weibull assumes failures can occur from t = 0. A three-parameter version adds a location parameter (γ, threshold life) for products that cannot fail before a minimum time. This is useful for fatigue and wear mechanisms.
β indicates the failure pattern: β < 1 is infant mortality (decreasing failure rate), β = 1 is random (constant rate, exponential), β > 1 is wear-out (increasing rate). Typical mechanical wear-out has β = 2–5.
η is the characteristic life — the time at which 63.2% of units have failed (or 36.8% survive). It anchors the distribution on the time axis. Larger η means longer life.
B10 is the time at which 10% of the population has failed (90% reliability). It is widely used in bearing applications (per ISO 281) and automotive specifications. Other B-lives (B1, B5, B50) work similarly.
Use Weibull probability plotting (graphical) or maximum likelihood estimation (statistical). Software like Minitab, JMP, or free tools like Weibull++ perform this analysis. You need at least 5–10 failure observations.
Yes, using suspended (censored) data. Units that haven't failed contribute information about what they survived. Software handles right-censored data routinely. More suspensions require more total test time.
Use exponential (β = 1) only when you have evidence of constant failure rate. For most mechanical, electrical, and structural components, Weibull with β ≠ 1 better represents reality. Default to Weibull.