Paste your failure times and fit a Weibull distribution by median-rank regression. Get the shape β, scale η, reliability R(t), B10/B50 life, MTTF and a Weibull probability plot — all client-side.
Paste your failure times and press Calculate to fit the Weibull distribution.
Watch: Reliability Analysis: Weibull and Life Data
Ten pump seals were run to failure. When should you plan replacements, and are the failures early-life or wear-out? Enter the lab to find out.
Paste the time-to-failure for each unit (hours, cycles, kilometres), one per line. You need at least three failures; more points give a better fit.
The calculator sorts failure times from shortest to longest and fits a line on a special reliability chart. The line's slope tells you the failure pattern, and where it crosses tells you the typical life.
The calculator works out survival odds at any time, plus key milestones like B10 life (10% failure point) and average time to failure. Enter a target time to see reliability there. Prefer maximum-likelihood fitting? Switch it on in Advanced options.
Weibull analysis is the workhorse of reliability engineering. By fitting a flexible two-parameter distribution to failure data, it tells you not just how long things last on average, but how the risk of failure changes over time — which is what drives sensible maintenance, warranty and design decisions.
Weibull analysis models time-to-failure using the Weibull distribution, defined by a shape parameter β and a scale parameter η. The shape tells you whether failures are early-life, random or wear-out; the scale (characteristic life) is the time by which about 63.2% of the population has failed. Together they let you estimate reliability at any time, B-life points and the mean life from a relatively small sample of failures.
Weibull analysis turns a set of failure times into a reliability picture. It ranks the failures, plots them on special scales, and fits a line whose slope is the shape factor (β) — the key to the failure pattern: below 1 means early-life failures, around 1 means random failures, and above 1 means wear-out. From the fit it estimates the characteristic life and the reliability at any time, plus 'B-life' values like B10 (the time by which 10% are expected to fail) that are handy for setting replacement intervals.
A maintenance team records the age (in operating hours) of 15 bearing failures. More fail early and after heavy use, with fewer failures in the middle — a classic wear-out pattern.
The Weibull model gives a shape parameter of 2.3 (wear-out failures, increasing with age) and a characteristic life of 4,200 hours — meaning 63% of bearings will have failed by that point.
What to do with this: Schedule preventive replacement at 3,000 hours, before the failure rate accelerates. You've just turned reactive maintenance into a planned programme backed by real data.
Reliability data drives warranty cost, spare-part planning and maintenance schedules. Weibull analysis converts a handful of failure times into actionable numbers — reliability at the warranty period, the right preventive-maintenance interval, and the expected life — so engineering and finance can plan with evidence rather than guesswork.
Use Weibull analysis whenever you have time-to-failure (or cycles-to-failure) data and want to understand life and reliability: qualifying a new component, setting a maintenance interval, estimating warranty exposure, or diagnosing whether failures are early-life, random or wear-out.
In DMAIC, Weibull analysis supports the Measure and Analyse phases of reliability-focused projects, quantifying baseline life and failure mode. In Design for Six Sigma it sets reliability targets and verifies them in testing, linking design decisions to field performance.
Use the shape β to choose a maintenance strategy: burn-in for β < 1, condition monitoring for β ≈ 1, and scheduled replacement near the B10 life for β > 1. Document the reliability at your warranty or design-life point, and feed the failure mode into a fishbone or FMEA to attack the root cause. Re-fit as more field data arrives to tighten the estimates.
Combine Weibull analysis with FMEA, control charts and a DMAIC structure to design, verify and sustain reliable products and processes.
Weibull analysis fits a Weibull distribution to time-to-failure (or life) data so you can model how a product or component fails over time. From two parameters — the shape β and the scale η (characteristic life) — you can estimate reliability at any time, the failure rate, characteristic life points such as B10 and B50, and the mean time to failure. It is the standard tool in reliability engineering because the same distribution can describe infant mortality, random failures and wear-out simply by changing the shape parameter.
The shape parameter β describes how the failure rate changes with time. β < 1 means a decreasing failure rate (infant mortality — early-life defects), so burn-in or screening helps. β ≈ 1 means a constant failure rate (random failures), equivalent to the exponential distribution, where preventive replacement does not help. β > 1 means an increasing failure rate (wear-out), so scheduled replacement or maintenance is worthwhile. Reading β is usually the first thing a reliability engineer does because it points directly to the right maintenance strategy.
B10 life is the time by which 10% of the population is expected to have failed — equivalently, the time at which reliability has dropped to 90%. It is widely used in bearings, gears and other mechanical components as a design-life target. This calculator also reports B50 life (the median life, 50% failed). With the fitted Weibull parameters, B10 = η × (−ln(0.9))^(1/β) and B50 = η × (−ln(0.5))^(1/β).
It uses median-rank regression on a Weibull probability plot. Failure times are sorted, each is assigned a median rank Fᵢ = (i − 0.3)/(n + 0.4), and the points (ln tᵢ, ln(−ln(1 − Fᵢ))) are fitted by ordinary least squares. The slope of that line is the shape β and the scale η is recovered from the intercept. This is a robust, transparent method for complete (uncensored) data. For a statistically efficient fit, switch to maximum-likelihood estimation (MLE) under Advanced options — it solves the Weibull likelihood equations numerically for β and η and is the preferred estimator once you have a reasonable number of failures. The rank-regression estimates stay on screen so you can compare the two.
A fitted Weibull model tells you how long things last and when they fail. Structured training shows you how to act on reliability data and build it into design and maintenance.
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