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Weibull Analysis Calculator
In short: Weibull analysis fits two parameters to your failure data — a shape β that reveals whether failures are early, random, or wear-out, and a scale η, the characteristic life. Paste failure times below and this tool returns β and η, MTTF, median and B10 life, reliability at any age, the hazard rate, and the failure regime.
Fit a Weibull distribution to failure data
failure times → shape β and scale η → R(t) = e−(t/η)β, MTTF, B10 life, and the failure regime
Fitted Weibull parameters
Shape parameter β = 2.554, η = 913.78 h
β > 1 — wear-out (increasing hazard). Scheduled preventive replacement is worthwhile.
What this calculator computes
This tool performs a two-parameter Weibull analysis, the standard method for turning a set of failure times into a complete picture of how a component fails over its life.
Give it the ages at which units failed and it estimates the two parameters that define the distribution: the shape, which reveals whether failures are early, random, or wear-out driven, and the scale, the characteristic life by which about sixty-three percent have failed.
From those two numbers it derives the mean time to failure, the median life, the B10 and any custom B-life you ask for, the reliability at a chosen age, and the instantaneous hazard, and it plots the survival curve so the whole failure pattern is visible at once.
What makes the Weibull distribution the workhorse of reliability engineering is its flexibility. A single family of curves, governed by that one shape parameter, can describe three completely different failure behaviours: the falling hazard of infant mortality, the flat hazard of random failure, and the rising hazard of wear-out. No other common distribution spans that range with so little machinery, which is why life-data analysis, warranty modelling, and maintenance planning all lean on it. The exponential model, familiar from constant-failure-rate work, is simply the Weibull with a shape of exactly one, so this calculator generalises that tool rather than competing with it.
What sets this calculator apart is that it does both halves of a real Weibull analysis and interprets the result. It does not merely accept a shape and scale you already know; it fits them from raw failure times using transparent median-rank regression and reports how well the model fits. And it does not stop at numbers; it names the failure regime the shape parameter implies and states the maintenance action that regime supports, so the output is a decision, not just a distribution. Everything runs in your browser with nothing stored, alongside a chart and PDF and CSV export.
How to use this calculator, step by step
Begin by choosing an input mode. In fit mode you paste your failure times, one per line or separated by commas, and the calculator estimates the shape and scale for you; this is the usual starting point when you have field or test data. In direct mode you type a shape and a scale you already know, from a datasheet, a handbook, or a previous analysis, and the calculator computes the life metrics and the curve without fitting. Both modes lead to the same set of outputs, so you can move between fitting from data and exploring a known distribution freely.
Next, set the two evaluation inputs. The first is the time at which you want the reliability, the age whose survival probability you care about; the second is a custom B-life percentage, such as five for the B5 age at which five percent have failed, which sits alongside the B10 the tool always reports. The calculator opens with a worked example already filled in, a set of ten wear-out failure times that fit to a shape of about 2.55 and a characteristic life near 914 hours, so you see a complete analysis immediately and can replace the data with your own.
The result panel leads with the fitted shape and scale, then lists the mean time to failure, the median life, the B10 and your custom B-life, the reliability and probability of failure at your chosen time, and the constant of the hazard at that age. When you are fitting from data it also reports the R-squared of the regression as a fit-quality check. A note names the failure regime the shape implies and the maintenance strategy it supports, the chart plots the full reliability curve, and you can download or share the analysis, all locally.
Reading the shape parameter: the heart of the analysis
Of everything a Weibull analysis produces, the shape parameter deserves your attention first, because it identifies the failure mechanism and therefore the correct response. It has no units and its value alone, before any life number, tells you which of three worlds you are in. A shape below one means the hazard rate falls as units age: the longer a unit has survived, the less likely it is to fail next, the classic signature of infant mortality driven by manufacturing or installation defects. In that world burn-in and tighter quality control pay off, and scheduled replacement of survivors is counterproductive because the survivors are the good ones.
A shape close to one means the hazard is essentially constant, failures arrive at random regardless of age, and the Weibull has collapsed into the exponential model. Here nothing about a unit’s past predicts its future, replacement on a schedule does nothing to reduce failures, and the right levers are redundancy and fast repair rather than time-based maintenance. A shape above one means the hazard rises with age, the fingerprint of wear-out from fatigue, corrosion, erosion, or aging, and this is the one regime where scheduled preventive replacement genuinely reduces failures, because units become more dangerous the longer they run and retiring them before the hazard climbs is worthwhile.
Because the shape carries this much meaning, it is worth reading it as a diagnosis rather than a number. A fitted shape of, say, 2.5 does not just parameterise a curve; it says the population is wearing out and that a preventive-replacement interval is a sensible thing to compute. A fitted shape near 0.7 says stop replacing good units and fix the early-life defect instead. The calculator states this interpretation in its note precisely so the shape is used the way reliability engineers use it, as the first and most consequential output of the whole analysis.
The scale parameter, characteristic life, and B-lives
The scale parameter, eta, anchors the distribution in time. It is the characteristic life, the age by which about 63.2 percent of the population has failed, and that figure holds no matter what the shape is, which makes eta a stable reference point. It shares the units of your failure times, so if you entered hours it is an age in hours, and it is usually close to, though a little above, the mean life for wear-out data. Changing eta simply stretches or compresses the whole failure pattern along the time axis without altering its shape, so it answers the question of when failures happen while the shape answers how they are distributed around that time.
For design and procurement, though, the mean and the characteristic life are often less useful than the B-lives, and this is where Weibull analysis earns its keep. A B-life is the age by which a stated fraction of the population has failed: B10 is the age at ten percent failed, B5 at five percent, B1 at one percent.
These are early-life durability figures, and they matter because a mean or a characteristic life is an age most units survive, whereas a B10 is an age you can promise as a floor with a known small failure fraction beneath it.
Bearing manufacturers quote B10 life for exactly this reason, and warranty engineers pick a B-life whose failure fraction matches an acceptable field-return rate.
This calculator always reports the B10 and lets you enter any B-life percentage you like, so you can size a warranty period, a service interval, or a replacement age to the specific failure fraction your risk tolerance allows rather than to an average. Reading eta, the mean, the median, and a B-life together gives the full temporal picture: eta and the mean say roughly how long the population lasts, the median splits it in half, and the B-life pins down the early tail where the first failures, the ones that usually drive warranty and safety decisions, occur.
How the fit works: median-rank regression
When you fit from data, the calculator uses median-rank regression, the method behind classic Weibull probability paper and the most transparent way to estimate the two parameters. The idea rests on a neat algebraic fact: if failure times really follow a Weibull distribution, then plotting the natural logarithm of time against the double logarithm of the survival fraction turns the curve into a straight line whose slope is the shape parameter and whose intercept fixes the scale. Fitting is therefore just fitting a line, which is why the method is exact, reproducible by hand, and needs no iterative solver.
The one subtlety is estimating the cumulative failure fraction for each observed failure. You cannot simply use the raw rank divided by the count, because that would put the last failure at one hundred percent, off the edge of the plot.
Instead the calculator uses Bernard’s median-rank approximation, which assigns each ordered failure a fraction of roughly its rank minus 0.3 divided by the count plus 0.4. This gives a well-behaved estimate of where each failure sits on the cumulative scale, and it is the same approximation drawn on printed Weibull paper for decades.
The calculator sorts your times, computes these median ranks, transforms both axes, fits a least-squares line, and reads off the shape from the slope and the scale from the intercept.
The regression also yields a coefficient of determination, the R-squared, which the calculator reports as a fit-quality measure.
A value very close to one means your data lie almost perfectly along the Weibull line and the two-parameter model describes them well; a noticeably lower value is a warning that a single Weibull may not capture the data, perhaps because two failure modes are mixed together or a location shift is present.
Median-rank regression is best suited to complete data, where every unit’s failure time is known; heavily censored data, with many units still running, are better handled by maximum-likelihood methods, and a low R-squared on obviously curved data is the cue to treat the simple fit with caution.
Five worked examples you can follow
Example 1: fitting wear-out data
The calculator opens with ten failure times ranging from 320 to 1330 hours. Fitting gives a shape of about 2.55 and a characteristic life near 914 hours, with an R-squared of 0.997, so the Weibull describes the data very well. The shape above two immediately says wear-out: the hazard is rising, failures cluster toward the middle and end of life, and a preventive-replacement interval is a sensible thing to compute from these numbers.
Example 2: reading the life metrics
From that same fit the mean time to failure is about 811 hours and the median about 792, both below the characteristic life of 914 as expected for wear-out data. The B10 life is about 379 hours and the B5 about 286, so ten percent of units are expected to fail by 379 hours and five percent by 286. If you were setting a conservative service interval to keep early failures rare, the B5 or B10 age, not the mean, is the figure to use.
Example 3: reliability at a chosen age
Evaluating reliability at 600 hours on the default fit gives about 71 percent, so roughly seven in ten units are expected to survive to 600 hours and about 29 percent to have failed by then. Changing the evaluation time traces the whole survival curve; pushing it out to the characteristic life of 914 hours drops reliability to about 37 percent, the e-to-the-minus-one landmark that holds at eta for any shape.
Example 4: a known distribution in direct mode
Switch to direct mode and enter a shape of one with any scale, say 1000 hours. The Weibull collapses to the exponential: the mean equals the scale at 1000 hours, the hazard is flat, and reliability at 1000 hours is the familiar 37 percent. This shows concretely that the exponential is the shape-equals-one slice of the Weibull, and it is a useful check that your intuition about the two models lines up.
Example 5: an infant-mortality fit
Enter a shape below one in direct mode, say 0.6, with a scale of 500 hours. The note flips to infant mortality: the hazard now falls with age, so a unit that has survived a while is safer than a new one, and the right response is burn-in or a quality fix rather than scheduled replacement. Seeing the regime label and the maintenance advice change with the shape is the quickest way to internalise why the shape parameter is the first thing to read.
Three expert tips for reliable results
Read the shape before the life numbers
The shape parameter tells you the failure mechanism and the right maintenance strategy. A mean life is meaningless until you know whether you are in infant mortality, random failure, or wear-out, so interpret the shape first.
Check the fit quality
A high R-squared means the Weibull line fits your data; a low one warns of mixed failure modes or a poor model. Do not trust parameters from an obviously curved plot without investigating why.
Use B-lives, not the mean, for early-failure decisions
Warranties and safety intervals care about the first few percent of failures, not the average. Size them to a B10 or B5 age so the failure fraction beneath your target is small and known.
The mathematics behind the results
The two-parameter Weibull distribution is defined by its reliability function, the probability of surviving to time t, which is the exponential of minus the quantity t divided by the scale, raised to the shape power.
The probability of failure is its complement, one minus that survival function, and the hazard rate, the instantaneous failure rate given survival so far, is the shape divided by the scale, times the ratio of time to scale raised to the shape minus one.
That hazard formula is the mathematical heart of the model’s flexibility: when the shape is less than one the exponent is negative and the hazard falls with time, when the shape equals one the hazard is constant at one over the scale, and when the shape exceeds one the hazard rises, all from a single expression.
The life metrics follow from the distribution. The mean time to failure is the scale multiplied by the gamma function evaluated at one plus the reciprocal of the shape, where the gamma function is the continuous generalisation of the factorial; the calculator evaluates it with a Lanczos approximation accurate to many digits.
The median life is the scale times the shape-th root of the natural log of two, and a general B-life at failure fraction p is the scale times the shape-th root of minus the natural log of one minus p, which is where the B10 and custom B-life come from.
At time equal to the scale the survival function is always the exponential of minus one, about 37 percent, which is why the scale is the 63.2-percent-failed characteristic life for every shape.
The fit itself is linear regression on transformed coordinates. Taking the natural log of time and the natural log of minus the natural log of the survival fraction linearises the Weibull, so a least-squares line through the median-rank points has the shape as its slope and an intercept from which the scale is recovered as the exponential of minus the intercept over the slope.
Two assumptions underlie the clean results: that a single Weibull distribution describes the data, which the R-squared checks, and that the data are complete rather than heavily censored, since median-rank regression on uncensored failures is what the tool implements.
Judging whether one Weibull fits, or whether mixed modes or censoring demand a more elaborate analysis, remains the analyst’s job.
Where Weibull analysis is used
Weibull analysis is used wherever the timing of failures carries information worth acting on, which is most of reliability engineering. In maintenance it turns field failure data into a shape parameter that says whether a preventive-replacement policy will help, and into B-lives that set the replacement age; a wear-out shape justifies a scheduled interval, while a random or infant-mortality shape tells you to spend the money elsewhere.
It connects directly to the rest of this silo: the shape-equals-one case is the exponential handled by the failure rate and reliability calculator, the characteristic life and MTTF relate to the mean life in the MTBF, MTTR and availability calculator, and the reliability at a chosen age is what the system reliability calculator combines across components.
Beyond maintenance, the distribution is a fixture of warranty and quality engineering. Warranty periods are set by choosing a B-life whose failure fraction matches an acceptable return rate, so a manufacturer who wants no more than five percent of units to fail within warranty sizes the term to the B5 age from a Weibull fit of test or field data.
In quality and root-cause work the shape parameter is a diagnostic: a fitted shape that points to infant mortality sends investigators toward process and assembly defects, while one that points to wear-out sends them toward material fatigue and design margins.
Reliability demonstration tests, accelerated life tests, and bearing and material fatigue studies all report Weibull parameters as their standard summary.
The method also underpins fleet and spares decisions. Knowing the shape and scale of a population’s failure distribution lets a planner forecast how many units will fail in a coming period, size a spares holding to a service level, and decide whether to replace a component preemptively or run it to failure.
Because the Weibull captures the full failure pattern rather than a single average, these forecasts respond correctly to age: a wearing-out fleet is predicted to shed failures at an accelerating rate as it ages, which a constant-rate model would miss entirely.
Return to the Maintenance and Reliability hub for the companion tools that turn these parameters into availability, redundancy, and maintenance-interval decisions.
Weibull, the exponential, and the bathtub curve
The clearest way to see where Weibull analysis fits is against the classic bathtub curve, which plots the hazard rate over the whole life of a population and shows three regions: a falling hazard early on, a flat hazard through useful life, and a rising hazard at the end. Each region corresponds to a range of the Weibull shape parameter. A shape below one produces the falling hazard of the infant-mortality region, a shape of exactly one produces the flat hazard of useful life, which is precisely the exponential model, and a shape above one produces the rising hazard of wear-out. A single Weibull fit therefore tells you which region of the bathtub your population currently occupies.
This unification is why the exponential is best understood as a special case rather than a separate model. The constant-failure-rate work that treats the hazard as flat, quotes an MTBF, and relies on the memoryless property is exactly the Weibull with a shape of one, and it is valid only in the flat middle of the bathtub.
When a Weibull fit returns a shape near one, that flat-hazard assumption is confirmed and the simpler exponential arithmetic is justified; when the fit returns a shape well away from one, the exponential would misstate reliability, and the Weibull is telling you so quantitatively.
In this sense a Weibull analysis is also a test of whether the easier exponential model may be used at all.
Two-parameter and three-parameter Weibull, and censored data
This calculator fits the two-parameter Weibull, which assumes failures can begin from time zero. In some situations a component is effectively failure-free for an initial period, a guaranteed minimum life before any unit can fail, and the data are better described by a three-parameter Weibull that adds a location, or shift, parameter to move the start of the distribution away from zero.
A tell-tale sign is a two-parameter probability plot that curves systematically rather than following a straight line; introducing a location shift often straightens it.
The two-parameter model is the right default for most work, but if your failures clearly do not begin until well after time zero, be aware that a shift parameter may improve the fit and that the two-parameter shape and scale will be biased if a real threshold is ignored.
The other practical limit is censoring. Median-rank regression as implemented here is built for complete data, where every unit in the sample has failed and its age is known. Real reliability data are frequently censored: units are still running when the study ends, or they are removed for reasons unrelated to the failure mode under study, so their eventual failure age is unknown.
Treating censored survivors as if they had failed, or simply dropping them, both distort the estimate, usually making the population look worse than it is. When a substantial fraction of units are censored, maximum-likelihood estimation, which uses the information that a survivor lasted at least as long as its censoring time, is the sounder method.
Use this calculator’s regression fit for complete or lightly censored datasets, and read a poor R-squared or a curved plot as a prompt to consider whether censoring or a location shift is the reason.
A short history of Weibull analysis
The distribution is named for Waloddi Weibull, a Swedish engineer who described it in a 1951 paper on the statistical distribution of material strength and fatigue life, arguing that a single flexible function could represent a wide range of failure phenomena. The idea was slow to catch on at first, but its ability to fit early-life, random, and wear-out failures with one adjustable shape made it increasingly attractive as reliability engineering matured through the mid-twentieth century, particularly in aerospace and materials work where fatigue life needed a distribution that a normal or exponential curve could not supply.
Its adoption accelerated with the spread of Weibull probability paper, which let engineers fit the distribution graphically by plotting median-rank points and drawing a line, reading the shape from the slope, long before computers made numerical fitting routine.
That graphical heritage is why median-rank regression, the method this calculator implements, remains a standard and intuitive approach.
Over the following decades Weibull analysis became the default framework for life-data analysis, embedded in reliability standards, warranty analysis, and the software packages that reliability engineers use daily, and the shape parameter’s role as a failure-mechanism diagnostic became part of the discipline’s common language.
Common mistakes to avoid
A few errors recur when people run a Weibull analysis. Watch for them.
- Quoting a life number before reading the shape. A mean or B-life is only meaningful once you know the regime; interpret the shape parameter first to see whether failures are early, random, or wear-out.
- Ignoring a poor fit. A low R-squared, or an obviously curved probability plot, signals mixed failure modes or a wrong model. Do not report parameters from a bad fit as if they were sound.
- Fitting heavily censored data with simple regression. Median-rank regression assumes mostly complete failure data; with many still-running units, maximum-likelihood methods are more appropriate.
- Treating the mean life as a typical or fifty-fifty age. The mean is not the median, and for wear-out data both sit below the characteristic life; use the median for the fifty-percent age.
- Mismatched time units. All failure times and the evaluation time must share one unit; mixing hours and cycles or days silently corrupts the scale and every life metric.
- Forcing a Weibull on infant-mortality data and then scheduling replacement. A shape below one means survivors are the good units; replacing them on a schedule wastes life and does not reduce failures.
Input format and quick reference
Choose fit mode to paste failure times, one per line or comma-separated in a single time unit, or direct mode to enter a shape and scale you already know. Set the evaluation time for R(t) and a custom B-life percentage. The reference below explains each output.
| Output | What it means |
|---|---|
| Shape parameter β | Failure regime: <1 infant mortality, ≈1 random (exponential), >1 wear-out |
| Scale η | Characteristic life; the age by which about 63.2% have failed |
| MTTF | Mean time to failure, η times the gamma of (1 + 1/β) |
| Median life (B50) | Age by which half the population has failed |
| B10 life | Age by which 10% have failed; reliability equals 90% |
| Reliability R(t) | Probability of surviving to the evaluation time |
| Hazard rate h(t) | Instantaneous failure rate at the evaluation time |
| Fit quality (R²) | How well the median-rank line fits your data; near 1 is good |
Frequently asked questions
What is Weibull analysis?
Weibull analysis is a method for describing how the failure risk of a component changes over its life, using a flexible probability distribution defined by two numbers: a shape parameter, written beta, and a scale parameter, written eta.
From a set of failure times it estimates those two parameters and, from them, everything else you want to know: the probability a unit survives to any age, the mean life, the median life, and the B-lives such as the B10 age by which ten percent have failed.
Its great strength is that a single model can represent early-life failures, purely random failures, and wear-out simply by changing the shape parameter, which is why it has become the default distribution in reliability engineering and life-data analysis.
What does the shape parameter beta tell me?
The shape parameter beta is the single most informative number in a Weibull analysis because it identifies the failure mechanism. When beta is less than one the hazard rate is falling with age, the signature of infant mortality, so failures cluster early and burn-in or better quality control helps.
When beta is close to one the hazard is constant, failures are random and age-independent, and the Weibull reduces exactly to the exponential model. When beta is greater than one the hazard is rising, the signature of wear-out from fatigue, corrosion, or erosion, and scheduled preventive replacement becomes worthwhile.
Reading beta first, before any life number, tells you which of these three regimes you are in and therefore which maintenance strategy the data actually supports.
What is the scale parameter eta, the characteristic life?
The scale parameter eta, also called the characteristic life, is the age by which about 63.2 percent of the population has failed, regardless of the shape parameter. It sets the horizontal scale of the distribution: doubling eta stretches the whole failure pattern out over twice the time without changing its shape.
The 63.2 percent figure is not arbitrary; it is one minus the reciprocal of the mathematical constant e, and it falls out of the Weibull formula at the point where time equals eta.
Because eta is expressed in the same units as your failure times, it is the most tangible single summary of how long the population lasts, and it is often close to, though not identical with, the mean life.
What is B10 life and how is it used?
B10 life is the age by which ten percent of a population is expected to have failed, or equivalently the time at which reliability drops to ninety percent. It is a widely used design and procurement figure, especially for bearings and other mechanical components, because it states an early-life durability target rather than an average that half the units will fall short of.
B-life notation generalises this: B5 is the age at five percent failed, B1 at one percent, and so on, letting you pick the failure fraction that matters for your risk tolerance. This calculator reports B10 by default and lets you enter any B-life percentage, so you can size a warranty or a replacement interval to a specific acceptable failure fraction rather than to the mean.
How does the calculator fit beta and eta from failure data?
When you use the fit mode, the calculator estimates beta and eta by median-rank regression, the classic and transparent Weibull-fitting method.
It sorts your failure times, assigns each one a median-rank estimate of the cumulative failure fraction using Bernard’s approximation, and then transforms the data so that a Weibull distribution becomes a straight line: the natural log of time on one axis and the double-log of the survival fraction on the other.
Fitting a least-squares line to those transformed points gives the shape parameter as the slope and the scale parameter from the intercept, and the R-squared of that line, which the tool reports, tells you how well the Weibull model fits your data. This method is exact, reproducible by hand, and needs no heavy statistical machinery, which is why it is the standard on Weibull probability paper.
How is Weibull related to the exponential model?
The exponential model is the special case of the Weibull that arises when the shape parameter equals exactly one. At that shape the hazard rate is constant, the memoryless property holds, and the scale parameter eta becomes identical to the mean time between failures. Everything the exponential reliability calculator does is therefore a single slice through the broader Weibull picture.
The value of the more general model is that it does not assume the shape is one; it estimates it from data, so it can reveal a falling or rising hazard that the exponential cannot represent.
In practice you can think of Weibull as the tool that tells you whether the exponential assumption is even valid: if the fitted shape comes out near one, the simpler exponential is justified, and if it does not, Weibull is the model you need.
What is MTTF and how does it relate to eta?
MTTF, the mean time to failure, is the average age at failure across the whole population, and for a Weibull distribution it equals the scale parameter eta multiplied by the gamma function of one plus the reciprocal of beta.
The gamma factor is close to one when beta is near one and dips to a minimum around 0.886 near a shape of two before rising again, so the mean life is usually somewhat less than the characteristic life eta for wear-out data.
MTTF is the right summary when you care about average consumption of life, for instance in costing or in spares forecasting, but it can be misleading on its own because it says nothing about spread; two populations with the same mean can have very different early-failure behaviour, which is exactly what the shape parameter and the B-lives capture.
When should I use Weibull instead of a simple average?
Use Weibull whenever the timing of failures matters and not just their average, which is almost always in serious reliability work. A simple mean life throws away the shape of the failure pattern: it cannot tell you whether failures are clustered early, spread randomly, or concentrated at end of life, and those distinctions drive completely different maintenance decisions.
If you only ever quote an average, you cannot distinguish a fleet shedding infant-mortality defects from one wearing out, even though the first calls for burn-in and the second for scheduled replacement.
Weibull keeps that information in the shape parameter and expresses it in decision-ready numbers like B10 life and reliability at a chosen age, which is why it is preferred over a bare average for warranty setting, maintenance planning, and root-cause work.
Does this calculator store the numbers I enter?
No. The calculator runs entirely in your browser. The failure times, shape and scale parameters, and any other values you enter are never sent to our servers, stored, or shared. You can download a PDF or CSV of your results locally, and nothing leaves your device. See our Privacy Policy for details.
Is the Weibull analysis calculator free?
Yes. The Weibull analysis calculator is completely free, with no account, sign-up, or usage limit. It fits the shape and scale parameters from your failure data or accepts them directly, and returns MTTF, median life, B10 and custom B-lives, reliability at a chosen time, the hazard rate, the failure regime, and the R(t) curve, with PDF and CSV export, all at no cost.
Related maintenance and reliability calculators
More tools in this silo. Return to the Maintenance and Reliability hub for the full set.
Sources, disclaimer and editorial transparency
This calculator applies the two-parameter Weibull model: R(t)=e^(−(t/η)^β), F(t)=1−R(t), hazard h(t)=(β/η)(t/η)^(β−1), MTTF=η·Γ(1+1/β), median=η(ln2)^(1/β), and B-life=η(−ln(1−p))^(1/β), with parameters fitted by median-rank (Bernard) regression, consistent with standard life-data analysis references. This calculator and guide are created and reviewed by the OpsCalculators team; see our Editorial Policy for how each tool is researched, built, and tested.
Results are accurate estimates for planning and education, not certified reliability or safety engineering advice, and they assume a single two-parameter Weibull distribution with complete (uncensored) failure data; heavily censored data are better analysed by maximum-likelihood methods. See our full Disclaimer. OpsCalculators.com is operated by MAFHH INTERNATIONAL LTD. Your data is processed in your browser and never stored; see our Privacy Policy.