Returns the Weibull distribution. Use this distribution in reliability analysis, such as calculating a device's mean time to failure.
Syntax
WEIBULL(x,alpha,beta,cumulative)
X is the value at which to evaluate the function.
Alpha is a parameter to the distribution.
Beta is a parameter to the distribution.
Cumulative determines the form of the function.
Remarks
- If x, alpha, or beta is nonnumeric, WEIBULL returns the #VALUE! error value.
- If x < 0, WEIBULL returns the #NUM! error value.
- If alpha ≤ 0 or if beta ≤ 0, WEIBULL 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 returns the exponential distribution with:
Example
The example may be easier to understand if you copy it to a blank worksheet.
How to copy an example
- Create a blank workbook or worksheet.
- Select the example in the Help topic.
Note Do not select the row or column headers.
Selecting an example from Help
- Press CTRL+C.
- In the worksheet, select cell A1, and press CTRL+V.
- To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.
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| A |
B |
| 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) |
| =WEIBULL(A2,A3,A4,TRUE) |
Weibull cumulative distribution function for the terms above (0.929581) |
| =WEIBULL(A2,A3,A4,FALSE) |
Weibull probability density function for the terms above (0.035589) |
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