# Weibull Distribution in Google Sheets

## What Is Weibull Distribution in Google Sheets?

The WEIBULL function in Google Sheets returns the Weibull distribution, a continuous probability distribution that is often used to model the failure rates of systems over time. In Google Sheets, WEIBULL is used to calculate the probability density function (PDF) or cumulative distribution function (CDF) of the Weibull distribution. It provides us with knowledge of the probability of an event occurring at a specific value (x) in the Weibull distribution. For instance, in the example below, we have a value of x = 25, alpha 4, beta 56, and we have to find the cumulative distribution. Hence, the fourth argument is TRUE.

Apply the formula =WEIBULL(B1,B2,B3,B4) in cell B5. You get the value 0.0389 ~. Thus, the WEIBULL function can be used to analyze the components produced in a factory and other areas where the failure time needs to be determined.

###### Key Takeaways
• The Weibull distribution is mostly used in statistical analysis to model the failure rates of different systems. Its syntax is =WEIBULL(x, alpha, beta, TRUE/FALSE). Here, β > 0 is the shape parameter while α > 0 is the scale parameter.
• Understanding the Weibull distribution is crucial for quality control, reliability engineering, life testing, etc. where failure rates must be estimated.
• The Weibull distribution in Google Sheets can provide valuable insights into the overall reliability of systems, thereby helping in the decision-making process.
• Parameter values affect the distribution which is used to model the different behaviors for a particular function.

### Weibull Distribution() Google Sheets Formula

The following is the syntax for the WEIBULL.DIST function.

=WEIBULL (x, alpha, beta, cumulative)

Arguments

1. x: (required) The value at which you want to evaluate the Weibull distribution.
2. alpha: (required) It represents the shape parameter of the Weibull distribution and must be a positive number.
3. beta: (required) It represents the scale parameter of the Weibull distribution and must be a positive number.
4. cumulative: (required) This argument specifies whether you wish to calculate the probability density (FALSE) or the cumulative distribution function (TRUE) of the Weibull distribution. The default value is set to TRUE.

Note: Alpha and beta must be greater than 0. The cumulative must be TRUE to use the cumulative distribution function and FALSE to use the probability density function.

The Weibull distribution is used in reliability analysis due to its ability to adapt to different situations. Depending on the parameters we supply, it is used to model different behaviors for a particular function. The parameters used in the distribution control the shape and scale of the probability density function. Several methods are used to measure the reliability of the data. However, the Weibull distribution is one of the best methods for analyzing life data.

### How to Use Weibull Distribution in Google Sheets?

We can use the Weibull Distribution in Google Sheets formula (similar to Weibull Distribution in Excel) either by entering the formula manually or through the menu. First, we will go ahead and enter the function manually.

Let us look at the steps for applying the Weibull distribution in Google Sheets. We are analyzing a factory’s product to determine its reliability. Data is collected on its operational lifespan until its failure. This data is used to calculate Weibull distribution in Google sheets. Here, let the lifespan be x. The values of alpha and beta have also been estimated. Let us predict the failure rate over time using the Weibull distribution.

Step 1: Enter the details as shown in the table below.

Step 2: Now, let us enter the formula by typing it manually in cell C5.

Insert the following formula.

=WEIBULL(B2, B3, B4, TRUE).

Step 3: Press Enter. You get the value of the cumulative distribution using the WEIBULL function.

Once such values are calculated, you can plot these values again lifespan values in a Google chart that will allow you to analyze trends and patterns that would be difficult to understand in pure data form. The distribution curve will help you understand essential events such as the mean time to failure or where the failure rate increases drastically.

The same formula can be entered in the Google sheet through its menu.

Step 1: Go to the Insert menu and click on ‘Function.’ From here, choose ‘Statistical’ in the menu that appears.

Step 2: Choose WEIBULL and enter the required parameters. Thus, you can enter the formula manually or through the Google Sheets menu.

### Examples

Let us look at some interesting examples to understand the WEIBULL distribution in Google sheets better.

#### Example #1

In this example, assume you are determining the performance of a calculator that has been manufactured in a factory. We must calculate the probability that it will run successfully without failure after a given number of hours.

Step 1:  The first step involves collecting data. Here, we are using the x values or hours of usage. Here, we have used values from 5000 hours to 6200 hours with increments of 100. We have entered the data in the Excel sheet.

Step 2: Let us estimate the values of alpha and beta at 0.7 and 800, respectively. Now, let us enter these in the Google sheet. Apply the following formula to visualize the failure value at 5000 hours in cell C2.

= WEIBULL.DIST(A2, \$F\$1, \$F\$2, TRUE)

Step 3: Press Enter. You get a cumulative value of 5000. It is the percentage that indicates the calculator will run at most 5000 hours.

The probability that the calculator won’t run more than 5000 hours is 92. 29%.

Step 4: Drag the formula through from B2 to B14 to get the values for the rest of the hours.

Step 5: Now, the success rate of running for so many hours can be calculated by the formula:

1-(failure rate)

Apply the formula =1-B2 in cell C2 and format it as a percentage. Grag the Autofill handle all the way up to B14 to find the success rate of running of the calculator for the hours specified in Column A.

The output assists you in visualizing the failure distribution, thereby guiding you to make informed decisions on product improvement.

#### Example #2

Let us look at the failure rates of a vehicle’s tire, which is considered for study on how to improve its effectiveness. We calculate the cumulative probability considering this WEIBULL distribution for the different failure times specified for the tire. We also have the alpha and beta values formulated.

Step 1: Let us consider this a WEIBULL distribution and calculate both the PDF and CDF. To calculate the PDF, write the following formula in the cell C2.

=WEIBULL(B2, \$E\$1, \$E\$2, TRUE)

Step 2: Press Enter. You will get the value in cell C2. Now, drag the Autofill handle and get the values for all the hours failed by the tire.

Step 3: Let us try to plot the data on a chart. Go to Insert-> Chart and choose Line chart.

You get a chart, as shown in the image below.

Step 4: To calculate the PDF, apply the formula in cell F2 and press Enter.

=WEIBULL(B2, \$E\$1, \$E\$2, FALSE).

Drag the formula to cell F11 to get the PDF value.

#### Example #3

As we all know, the WEIBULL distribution is a probability distribution of random variables. We have a magnetic disk, and we have to check the probability it will last for 160 hours. Let us calculate the probability density function with an alpha value of 2.4 and a beta value of 1000.

Step 1: Let us formulate the details in a Google sheet.

Step 2: The alpha and beta values can be obtained by complex mathematical calculations. Enter the following formula in cell B4.

Step 3: Press Enter. You get the CDF value.

Now, to find the rate at which it will work successfully at 500 hours, subtract the value from 1.

### Important Things To Note

1. The shape parameter indicates the failure rate in the Weibull distribution. If beta < 1, the failure rate decreases with time, which cannot be the case. When beta > 1, the failure rate increases with time.
2. The x value is the time at which you calculate the failure rate; it must always be a positive number, or else you get the #NUM error.
3. We get the #Value! error if any of the arguments are non-numeric.
4. Weibull analysis is one of the examples of Weibull Distribution, which is very useful in Warranty Analysis, Utility Services, etc.

1. What are the uses of WEIBULL distribution in Google Sheets?

WEIBULL distribution in Google Sheets forecasts the lifespan of industrial machinery and also determines the failure rates of consumer electronics. It finds use in financial risk assessment, healthcare prognosis models, and in designing robust systems showcasing its versatility and adaptability across sectors.

2. What are the errors you get with the Weibull distribution in Google sheets?

If the arguments x, alpha, or beta are non-numeric, the WEIBULL function returns the #VALUE! error. If the value of x < 0, WEIBULL returns the #NUM! error. It also returns the #NUM error if alpha ≤ 0 or beta ≤ 0.

3. How to calculate Weibull distribution in Google sheets?

In Google Sheets, the function WEIBULL calculates the probability density (PDF) or cumulative distribution function (CDF) of the Weibull distribution. You have to enter the following formula in any cell of the Excel sheet.
=WEIBULL(x, alpha, beta, cumulative)
If the cumulative argument is set to TRUE, the WEIBULL function calculates the cumulative probability that a random variable that is Weibull-distributed is less than or equal to the value x. If it is set to FALSE, it calculates the probability density at the value x.