The Weibull Distribution is a probability distribution that is frequently used in engineering.
The Weibull probability density function is given by the equation:
where x is the independent variable, α is the shape parameter, and β is the scale parameter.
The Weibull cumulative distribution function is:
More information on the Weibull Distribution is given on the Wikipedia Weibull Distribution PageThe Excel WEIBULL.DIST function calculates the Weibull Probability Density Function or the Weibull Cumulative Distribution Function for a supplied set of parameters.
Although the function is new in Excel 2010, it is simply a renamed version of the Weibull function, which is available in Excel 2007 and earlier.
The format of the Weibull.Dist 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, α = 3 and the scale parameter, β = 1.
If you want to calculate the value of this function at x = 1, this can be done with the Weibull.Dist function, as follows:
=WEIBULL.DIST( 1, 3, 1, FALSE )
This gives the result 1.10363832351433.
The above chart on the right shows the Weibull Cumulative Distribution Function with the shape parameter, α = 5 and the scale parameter, β = 1.5.
If you want to calculate the value of this function at x = 2, this can be done with the Weibull.Dist function, as follows:
=WEIBULL.DIST( 2, 5, 1.5, TRUE )
This gives the result 0.985212776817482.
The Excel Weibull.Dist function is described further on the Microsoft Office website.
If you get an error from the Excel Weibull.Dist function this is likely to be one of the following :
#NUM!    Occurs if either:

#VALUE!    Occurs when either of the supplied alpha or beta arguments are nonnumeric 