The WEIBULL function in Google Sheets is a powerful tool for calculating the Weibull distribution, widely used in reliability analysis and life data modeling. This function allows users to evaluate probabilities and values based on specific shape and scale parameters, making it essential for statistical analysis, risk assessment, and forecasting.

Syntax

WEIBULL(x, α, β, cumulative)  
 
x: The value at which to evaluate the function.
 
α: The shape parameter, which influences the form of the distribution.
 
β: The scale parameter, which stretches or compresses the distribution.
 
cumulative: A boolean value that determines the type of function to evaluate (TRUE for cumulative, FALSE for the probability density function).
 

Example #1

=WEIBULL(10, 2, 3, TRUE)  

This formula calculates the cumulative Weibull distribution at x=10 with shape parameter α=2 and scale parameter β=3, resulting in a value of approximately 0.703. This indicates that the probability of observing a value less than or equal to 10 is about 70.3%.

Example #2

=WEIBULL(5, 1, 1, FALSE)  

This function call computes the probability density at x=5 with shape parameter α=1 and scale parameter β=1. The result is about 0.206, which reflects the likelihood of exactly obtaining a value of 5.

Example #3

=WEIBULL(15, 3, 4, TRUE)  

Here, the formula returns the cumulative probability at x=15 with shape α=3 and scale β=4, resulting in approximately 0.843. This shows a high probability of observing a value of 15 or less.

Error handling

• NUM! This error occurs if the shape parameter α is less than or equal to 0, which is invalid for the Weibull distribution.
• VALUE! This error appears if non-numeric inputs are provided in any parameter, indicating an issue with the data type.
• N/A Caused when the specified ‘cumulative’ parameter is not a boolean value, requiring TRUE or FALSE.

Conclusion

The WEIBULL function in Google Sheets is an essential statistic tool for those working with probabilistic models and reliability data. Whether you’re assessing risks or modeling lifetimes of products, understanding how to use this function can greatly enhance your analytical capabilities. With its straightforward syntax and powerful applications, users can effectively leverage the Weibull distribution to extract valuable insights.