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#Statistical

WEIBULL.DIST

Excel Functions

Get the PDF or CDF of the Weibull distribution.

Syntax

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

Arguments

Parameter Description
x The value at which to evaluate the distribution (must be ≥ 0).
alpha The shape parameter of the distribution (must be > 0).
beta The scale parameter of the distribution (must be > 0).
cumulative A logical value that determines the form of the function. If TRUE, returns the cumulative distribution function; if FALSE, returns the probability density function.

Return Value

A number representing the probability density or cumulative probability value.

Details

The WEIBULL.DIST function calculates values for the Weibull distribution, which is a continuous probability distribution used to model the time until a specified event, such as the failure of a machine part. The Weibull distribution is especially useful in reliability analysis and life data analysis, as it can model increasing, constant, or decreasing failure rates depending on the value of the shape parameter (alpha). Suppose you are analyzing the lifetimes of a batch of light bulbs. Historical data suggests that the lifetimes follow a Weibull distribution with a shape parameter (alpha) of 1.5 and a scale parameter (beta) of 1000 hours. You want to know the probability that a randomly selected bulb will fail within 800 hours. To calculate this probability, use the cumulative distribution

Examples

Example #1 - Light bulb lifetime analysis

To calculate this probability, use the cumulative distribution function (CDF):

EXCEL 
=WEIBULL.DIST(800, 1.5, 1000, TRUE) // returns 0.511
Example #1 - Light bulb lifetime analysis

To find the probability that a bulb lasts longer than 800 hours, subtract the CDF from 1:

EXCEL 
=1-WEIBULL.DIST(800, 1.5, 1000, TRUE) // returns 0.489
Example #3 - Effect of scale parameter (beta)

For example, consider different brands of light bulbs with varying quality levels. All follow a Weibull distribution with shape parameter alpha = 2.0

EXCEL 
=WEIBULL.DIST(800, 2.0, 1000, TRUE)   // returns 0.473
=WEIBULL.DIST(800, 2.0, 1500, TRUE)   // returns 0.198
=WEIBULL.DIST(800, 2.0, 2000, TRUE)   // returns 0.095
Example #4 - Cumulative vs. probability density
EXCEL 
=WEIBULL.DIST(2.5, 5.0, 2.0, FALSE) // returns 0.289 (PDF)
Example #4 - Cumulative vs. probability density
EXCEL 
=WEIBULL.DIST(2.5, 5.0, 2.0, TRUE)  // returns 0.953 (CDF)
Example #4 - Cumulative vs. probability density

Using the CDF, you can calculate probabilities for different scenarios. To calculate the probability of an event occurring below a threshold:

EXCEL 
=WEIBULL.DIST(threshold, alpha, beta, TRUE)

See Also

GAMMA.DIST EXPON.DIST