Weibull Analysis Calculator
Fit grouped and censored lifetimes with complete observations and declared model limits.
Try before you buy.
- Free preview: the fitted shape in full with the model’s notes, a watermarked probability plot and the first rows of the field table; every other figure is hidden.
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Failure and suspension data
Your inputs stay on this device, and every result states the model it assumes.
Your records
CSV input
A blank frequency means one unit. Failures and suspensions need their time; intervals need both ends and are never turned into failures at their midpoint. Every other column and cell of your CSV is kept in the backup and the results.
Your inputs
Saving and restoring your own inputs never needs a pass. Reset clears this page: download a backup first.
Engineering estimate — not a professional design, safety approval or verification certificate. Review the stated independence, censoring and sampling assumptions with a qualified engineer.
In the CSV, text that starts like a spreadsheet formula is escaped so that it cannot run; the “Original value JSON” column keeps your exact text. A chart too large for one PNG downloads as overlapping tiles with an index.
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Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the Weibull Analysis Calculator
Fit a two-parameter Weibull model, or a three-parameter model with an explicitly bounded threshold search, to your complete life records. Exact failures, right suspensions and grouped frequencies retain their different meanings. Maximum likelihood includes survival exposure and complete failure-interval probabilities; median-rank regression uses censor-adjusted observed failure ranks. Read shape, scale, B1, B10, MTTF, query reliability and both conditional and unconditional period probabilities together with the fitting and confidence method.
How to use it
- Enter one retained record per failure, suspension or interval group, including its full frequency. All times use the same units.
- Choose maximum likelihood or median-rank regression. For three parameters, declare a finite threshold interval below every failure and a positive shape constraint.
- Inspect the probability chart, full records and diagnostics. Confidence methods and their sampling assumptions are stated separately from the point-fitting method.
- Keep an original-input backup. Unlock this result to copy the complete calculation or download CSV, PNG and PDF.
Examples
Exact failures at 1 and 2 time units, with a suspension at 3; shape fixed at 1 for the illustration
The exponential likelihood scale is total exposure 6 divided by 2 failures: 3 time units, rather than the failure-only mean 1.5.
Complete life likelihood
For x = t - location > 0, survival S(t) = exp(-(x/scale)^shape), and failure density f(t) = shape/scale × (x/scale)^(shape-1) × S(t). Exact failures contribute log f, suspensions log S, and failure intervals log[S(lower)-S(upper)], each multiplied by its retained frequency. Bp = location + scale × [-ln(1-p)]^(1/shape). See NIST Weibull maximum likelihood.
Rank regression and confidence
The plotted rank line uses Johnson censor-adjusted failure ranks and Bernard (rank-0.3)/(N+0.4) positions. Its slope is shape and its intercept determines scale. Regression software confidence intervals assume a different stochastic model and are not valid lifetime confidence bounds. The confidence calculation identifies its likelihood-based reference fit and assumptions; see NIST graphical estimation.
Threshold and period meaning
An unrestricted three-parameter likelihood can fail to have a finite optimum when the threshold approaches the earliest exact failure. A declared closed interval strictly below failures is a constrained model, including decreasing-hazard shapes below one. Period failure probability is S(start)-S(end); conditional failure given survival to start is 1-S(end)/S(start). The two quantities answer different questions.
Limitations
- Engineering estimate — not a professional design, safety approval or verification certificate. Confirm the model and sampling assumptions with a qualified engineer.
- Units are assumed to fail independently under the same conditions. Mixed failure modes and accelerated tests need models of their own.
- Reset clears the page: download a backup of your inputs to keep them.
Privacy
On this device; its files download once
Calculations and the files you open stay on this device: nothing is uploaded. Downloading a backup of your own inputs never needs a pass.
Frequently asked questions
What do I get without a pass?
Without a pass, Weibull Analysis Calculator shows the fitted shape in full with the model’s notes, a watermarked probability plot and the first rows of the field table; every other figure is hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
Should I omit a unit that has not failed?
Retain it as a suspension at its observed operating time. Its survival contribution changes the likelihood and the exposure; dropping it can bias the estimate.
What do shape values below and above one mean?
A fitted shape below one indicates decreasing hazard, one indicates constant hazard, and above one indicates increasing hazard in this Weibull model. It does not diagnose a particular physical failure mechanism.
Why do rank regression and maximum likelihood differ?
They optimize different criteria. The rank line fits plotting positions; likelihood fits observed failures and censoring probabilities. The page identifies both the chosen point method and the confidence reference.
Does a small sample give dependable B1 life?
A tail-life estimate can be very uncertain with few observed failures. Review the warnings and confidence assumptions with a qualified reliability engineer.