The WEIBULL.DIST function in Google Sheets is used to calculate the Weibull distribution, a versatile tool often employed in reliability analysis and modeling. This function can help in predicting the probability of failure at any given time, making it valuable for various engineering, manufacturing, and risk assessment applications.

Syntax

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

• x: The value at which you want to evaluate the function.
• alpha: The scale parameter, which must be greater than 0.
• beta: The shape parameter, which must also be greater than 0.
• cumulative: A boolean value that determines the form of the function. Use TRUE to get the cumulative distribution function and FALSE to get the probability density function.

Example #1

WEIBULL.DIST(1, 2, 3, TRUE)

This function calculates the cumulative distribution for a value of 1, given an alpha of 2 and a beta of 3. The result, based on real data, might be approximately 0.865. This indicates that there is an 86.5% probability of a failure occurring before time 1.

Example #2

WEIBULL.DIST(1, 1.5, 2, FALSE)

This instance calculates the probability density function for the value of 1 with parameters alpha of 1.5 and beta of 2. The resultant value could be around 0.199. This implies a specific likelihood of failure occurring exactly at time 1.

Example #3

WEIBULL.DIST(5, 3, 1, TRUE)

Here, the function evaluates the cumulative distribution for a value of 5 with alpha set to 3 and beta to 1. The output might be roughly 0.942, indicating a 94.2% chance of failing before time 5.

Error handling

• NUM!: This error occurs when either the alpha or beta parameters are less than or equal to zero, which is not valid for the Weibull distribution.
• VALUE!: This error appears if the parameters are not of the correct type (for example, if a text string is provided instead of a number).
• N/A: This may happen if the x value is not a valid number for the given parameters.

Conclusion

The WEIBULL.DIST function is a powerful statistical tool for analyzing failure rates and reliability in various fields. By leveraging its parameters, users can model real-world phenomena effectively, thus enabling informed decision-making based on statistical data.