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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:

## Examples

X

Alpha

Beta

Formula

Description (Result)

105

20

100

=WEIBULL([X],[Alpha],[Beta],TRUE)

Weibull cumulative distribution function for the specified arguments (0.929581)

105

20

100

=WEIBULL([X],[Alpha],[Beta],FALSE)

Weibull probability density function for the specified arguments (0.035589)

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