The Excel WEIBULL Function

Weibull Distribution

The Weibull distribution is a probability distribution that is frequently used in engineering.

The Weibull probability density function is :

Weibull Probability Density Function

where x is the independent variable, α is the shape parameter, and β is the scale parameter.

The Weibull cumulative distribution function is :
Weibull Cumulative Distribution Function
More information on the Weibull Distribution is given on the Wikipedia Weibull Distribution Page

WEIBULL and WEIBULL.DIST

In Excel 2010, the WEIBULL function has been renamed the WEIBULL.DIST function.

Although it has been replaced, the Weibull function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel.


Basic Description

The Excel WEIBULL function calculates the Weibull Probability Density Function or the Weibull Cumulative Distribution Function for a supplied set of parameters.

The format of the function is :

WEIBULL( x, alpha, beta, cumulative )

Where the function arguments are listed in the following table:

x - The value at which the function is to be calculated (must be ≥ 0)
alpha - The Shape parameter to the distribution (must be > 0)
beta - The Scale parameter to the distribution (must be > 0)
cumulative - A logical argument which denotes the type of distribution to be used;
TRUE = Weibull Cumulative Distribution Function
FALSE = Weibull Probability Density Function


Weibull Function Examples

Example 1 - Weibull Probability Density Function

The chart on the right shows the Weibull Probability Density Function with the shape parameter, alpha set to 3 and the scale parameter, beta set to 1.

If you want to use Excel to calculate the value of this function at x = 1, this can be done with the Weibull function, as follows:

=WEIBULL( 1, 3, 1, FALSE )

This gives the result 1.10363832351433.
Plot of Weibull Probability Density Function with Alpha=3 and Beta=1

Weibull Probability Density Function with α = 3 and β = 1

Example 2 - Weibull Cumulative Distribution Function

The chart on the right shows the the Weibull Cumulative Distribution Function with the shape parameter, alpha set to 5 and the scale parameter, beta set to 1.5.

If you want to use Excel to calculate the value of this function at x = 2, this can be done with the Weibull function, as follows:

=WEIBULL( 2, 5, 1.5, TRUE )

This gives the result 0.985212776817482.
Plot of Weibull Cumulative Distribution Function with Alpha=5 and Beta=1.5

Weibull Cumulative Distribution Function with α = 5 and β = 1.5

Further information and examples of the Excel Weibull function can be found on the Microsoft Office website.


Weibull Function Errors

If you get an error from the Excel Weibull function this is likely to be one of the following :

Common Errors
#NUM! - Occurs if either:
- the supplied x value is < 0
or
- the supplied alpha or the supplied beta argument is ≤ 0
#VALUE! - Occurs when either of the supplied alpha or beta arguments are non-numeric
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