WEIBULL.DIST Function

Excel Functions › Statistical

Excel 2010+ Statistical

The Excel WEIBULL.DIST function returns the Weibull distribution — widely used in reliability engineering to model failure rates and time-to-failure for components and systems.


Quick answer:
=WEIBULL.DIST(105,20,100,TRUE) cumulative probability = 0.9296

Syntax

=WEIBULL.DIST(x, alpha, beta, cumulative)
ArgumentDescription
xRequiredThe value at which to evaluate the distribution (must be ≥ 0). Often a time or life span.
alphaRequiredThe shape parameter (α > 0). α < 1 models a falling failure rate, α = 1 a constant rate (exponential), α > 1 a rising rate (wear-out).
betaRequiredThe scale parameter (β > 0), the characteristic life at which about 63.2% of units have failed.
cumulativeRequiredTRUE for the cumulative distribution (CDF); FALSE for the probability density (PDF).

How to use it

The cumulative flag picks between the two forms of the distribution. TRUE gives the probability that a unit fails at or before x; FALSE gives the density (the height of the curve) at x.

=WEIBULL.DIST(105,20,100,TRUE) // CDF = 0.9296
=WEIBULL.DIST(105,20,100,FALSE) // PDF = 0.0356

With a shape alpha of 20 and scale beta of 100, the example models a part that wears out sharply near 100 hours: by 105 hours about 93% have failed. The shape parameter is the heart of the model — values above 1 describe components that get more likely to fail as they age.

Special case: when alpha = 1 the Weibull distribution reduces to the exponential distribution, so =WEIBULL.DIST(x,1,beta,TRUE) matches =EXPON.DIST(x,1/beta,TRUE).

Try it: interactive demo

Live demo

Pick a WEIBULL.DIST example to see the formula and its result.

Result:

Practice workbook

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Frequently asked questions

What is the difference between WEIBULL.DIST and the old WEIBULL?
They compute the same distribution. WEIBULL.DIST is the modern name introduced in Excel 2010; the legacy WEIBULL is kept in the Compatibility category for older workbooks. Use WEIBULL.DIST going forward.
What do the alpha and beta parameters mean?
alpha is the shape parameter (the failure-rate trend) and beta is the scale parameter, the characteristic life at which roughly 63.2% of units have failed.
When should I use TRUE vs FALSE for cumulative?
Use TRUE for the cumulative probability of failing by time x — the usual reliability question. Use FALSE for the probability density at x, mainly when plotting the curve.
Does WEIBULL.DIST return an error for negative x?
Yes — x must be ≥ 0 and both alpha and beta must be > 0. A negative x or non-positive parameter produces a numeric error.

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Related functions: EXPON.DIST · GAMMA.DIST · POISSON.DIST · NORM.DIST · LOGNORM.DIST