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 |