# WEIBULL.DIST

The `WEIBULL.DIST` function returns the Weibull distribution, which is commonly used in reliability analysis to model time-to-failure data. It describes a range of possible times until failure for a product or process. The function returns the cumulative distribution function (CDF) if cumulative is TRUE, and the probability density function (PDF) if cumulative is FALSE.

## Usage

Use the `WEIBULL.DIST` formula with the syntax shown below, it has 3 required parameters and 1 optional parameter:

Parameters:
1. x (required):
The value at which to evaluate the function; must be greater than or equal to zero.
2. shape (required):
The shape parameter of the distribution; must be greater than zero.
3. scale (required):
The scale parameter of the distribution; must be greater than zero.
4. cumulative (optional):
A logical value that determines the form of the function to be returned; TRUE for the CDF, FALSE for the PDF. If omitted, defaults to TRUE.

## Examples

Here are a few example use cases that explain how to use the `WEIBULL.DIST` formula in Google Sheets.

### Calculate the probability of failure within a given time frame

Suppose you want to know the probability that a product will fail within the first 1000 hours of use, given that its Weibull shape parameter is 1.5 and its scale parameter is 500 hours. You can use `WEIBULL.DIST` to calculate this probability.

### Model the reliability of a system

If you know the Weibull distribution parameters for a system, you can use them to model its reliability over time. For example, you can use `WEIBULL.DIST` to calculate the probability that a system will still be operational after a certain amount of time has elapsed.

### Determine the expected value of a sample

If you have a sample of data that is known to follow a Weibull distribution, you can use `WEIBULL.DIST` to determine its expected value. This can be useful in predicting future values or comparing different samples.

## Common Mistakes

`WEIBULL.DIST` not working? Here are some common mistakes people make when using the `WEIBULL.DIST` Google Sheets Formula:

### Forgetting to convert units

If your data is in hours but you're using a scale parameter that assumes minutes, your results will be incorrect. Make sure your units are consistent throughout your analysis.

### Using the wrong type of distribution

Make sure the Weibull distribution is appropriate for your data. If your data follows a different distribution, using the `WEIBULL.DIST` function will give you incorrect results.

The following functions are similar to `WEIBULL.DIST` or are often used with it in a formula:

• `WEIBULL`

The `WEIBULL` function returns the Weibull distribution, which is a continuous probability distribution that is often used to model failure rates of systems over time. The function takes four arguments: `x`, which is the value at which to evaluate the distribution; `shape`, which is the shape parameter of the distribution; `scale`, which is the scale parameter of the distribution; and `cumulative`, which is a logical value indicating whether to return the cumulative distribution function (TRUE) or the probability density function (FALSE).

• `EXPON.DIST`

The EXPON.DIST function returns the exponential distribution of a specified random variable, x, given a specified lambda, LAMBDA. The exponential distribution is commonly used to model the time between events in a Poisson process. The function returns the probability density function or the cumulative distribution function of the exponential distribution depending on whether the cumulative argument is set to TRUE or FALSE. This function is useful for analyzing reliability data and can be used to determine the probability that a component will fail before a certain time.

You can learn more about the `WEIBULL.DIST` Google Sheets function on Google Support.