WEIBULL

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:

Equation

  • The equation for the Weibull probability density function is:

Equation

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

Equation

Example

The example may be easier to understand if you copy it to a blank worksheet.

ShowHow 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

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)
 
 
Applies to:
Excel 2003