# WEIBULL.DIST function

This article describes the formula syntax and usage of the WEIBULL.DIST function in Microsoft Excel.

Returns the Weibull distribution. Use this distribution in reliability analysis, such as calculating a device's mean time to failure.

## Syntax

WEIBULL.DIST(x,alpha,beta,cumulative)

The WEIBULL.DIST function syntax has the following arguments:

• X     Required. The value at which to evaluate the function.

• Alpha     Required. A parameter to the distribution.

• Beta     Required. A parameter to the distribution.

• Cumulative     Required. Determines the form of the function.

## Remarks

• If x, alpha, or beta is nonnumeric, WEIBULL.DIST returns the #VALUE! error value.

• If x < 0, WEIBULL.DIST returns the #NUM! error value.

• If alpha ≤ 0 or if beta ≤ 0, WEIBULL.DIST returns the #NUM! error value.

• The equation for the Weibull cumulative distribution function is:

• The equation for the Weibull probability density function is:

• When alpha = 1, WEIBULL.DIST returns the exponential distribution with:

## Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

 Data Description 105 Value at which to evaluate the function 20 Alpha parameter to the distribution 100 Beta parameter to the distribution Formula Description (Result) Result =WEIBULL.DIST(A2,A3,A4,TRUE) Weibull cumulative distribution function for the terms above (0.929581) 0.929581 =WEIBULL.DIST(A2,A3,A4,FALSE) Weibull probability density function for the terms above (0.035589) 0.035589
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