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WEIBULL Function

Excel 2007+

Summary

The WEIBULL function calculates the Weibull distribution, widely used in reliability engineering to model time-to-failure data for products and systems. It provides both probability density and cumulative distribution values essential for life testing and survival analysis.

Syntax

WEIBULL(x, alpha, beta, cumulative)

Parameters

Parameter	Type	Required	Description
x	`Number`	Yes	Value at which to evaluate the distribution (must be ≥ 0)
alpha	`Number`	Yes	Shape parameter of the Weibull distribution (must be > 0)
beta	`Number`	Yes	Scale parameter of the Weibull distribution (must be > 0)
cumulative	`Boolean`	Yes	TRUE for cumulative distribution function (CDF), FALSE for probability density function (PDF)

Using the WEIBULL Function

WEIBULL is essential for reliability analysis, calculating the probability that a device will fail before a certain time or the probability density at a specific point. Use TRUE for cumulative probability (CDF) to find failure probability up to time x, or FALSE for probability density function (PDF) to analyze failure rate at exact time x.

Common WEIBULL Examples

Cumulative Distribution (CDF)

=WEIBULL(105,20,100,TRUE)

Calculates cumulative probability of failure by time 105 (Result: 0.929581)

Probability Density Function (PDF)

=WEIBULL(105,20,100,FALSE)

Calculates probability density at exactly time 105 (Result: 0.035589)

Exponential Distribution Case

=WEIBULL(50,1,75,FALSE)

When alpha=1, returns exponential distribution PDF value

Frequently Asked Questions

When alpha=1, WEIBULL returns the exponential distribution, useful for constant failure rate modeling.

WEIBULL is legacy but functional. Microsoft recommends WEIBULL.DIST for improved accuracy and future compatibility.

TRUE returns the cumulative distribution function (CDF) - probability of failure before time x.

Common Errors and Solutions

#NUM!

Cause: x < 0, alpha ≤ 0, or beta ≤ 0

Solution: Ensure x ≥ 0 and both alpha and beta > 0

#VALUE!

Cause: Non-numeric input for x, alpha, beta

Solution: Use valid numeric values for all numeric parameters

Notes

Legacy function - consider WEIBULL.DIST for new workbooks
Essential for reliability engineering and quality control
When alpha=1, models constant failure rate (exponential)
Alpha < 1 = decreasing failure rate, Alpha > 1 = increasing failure rate

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Excel 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+