The Weibull distribution is a probability distribution that is frequently used in engineering.
The Weibull probability density function is:
where x is the independent variable, α is the shape parameter, and β is the scale parameter.
The Weibull cumulative distribution function is:
Further information on the Weibull Distribution is provided on the Wikipedia Weibull Distribution PageIn 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.
The Excel WEIBULL function calculates the Weibull Probability Density Function or the Weibull Cumulative Distribution Function for a supplied set of parameters.
The syntax of the function is:
Where the function arguments are:
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;

The above 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 calculate the value of this function at x = 1, this can be done with the Excel Weibull function, as follows:
This gives the result 1.10363832351433.
The above 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:
This gives the result 0.985212776817482.
Further information and examples of the Excel Weibull function are provided on the Microsoft Office website.
If you get an error from the Excel Weibull function this is likely to be one of the following:
#NUM!    Occurs if either:

#VALUE!    Occurs if any of the supplied arguments are nonnumeric. 