How to Use WEIBULL Function in Google Sheets

The WEIBULL function in Google Sheets is useful when you need to get the value of the Weibull distribution function for a given shape and scale.

A Weibull distribution is a continuous probability distribution most commonly used to analyze life data, model failure times, and assess product reliability. 

The rules for using the WEIBULL function in Google Sheets are as follows:

  • The function requires four arguments: x, shape, scale, and cumulative.
  • The function then outputs a number that corresponds to the value of the Weibull distribution with input x for the provided shape and scale.

Unlike a normal distribution, the Weibull function can also model skewed data. This flexibility allows you to model both left-skewed and right-skewed data. This is achieved by modifying the shape and scale parameters.

The shape parameter is also known as the Weibull slope. If the shape parameter is less than 1, it models a distribution of steadily decreasing values. A shape value between  1 to 2.6 resembles a right-skewed distribution.

The shape of the distribution approaches a normal distribution as you get closer to the value of 3. Values greater than three create a left-skewed distribution plot.

The scale parameter affects how far the probability distribution stretches out. Increasing the scale decreases the height and stretches the distribution further to the right.

Let’s take a look at a quick example of a situation where we can use the WEIBULL function to model our probabilities.

In reliability analysis, we aim to make predictions about the life of products in a population using data from a representative sample of units. As a mobile phone manufacturer, you want to reach the desired reliability of 0.9 at 10,000 cycles. This means that 90% of your manufactured phones should survive at least 10,000 cycles.

With the WEIBULL function, we can model this probability distribution and make predictions of the survival rate of your products given a unit of time or number of cycles.

For example, let’s assume that the Weibull distribution for a laptop has an alpha of 1000 hours and a beta of .6. What is the probability that the laptop will last over 5000 hours? The WEIBULL function can easily solve this for us.

This use case is just one way to use the WEIBULL function in Google Sheets. The Weibull distribution is quite versatile, finding applications in various fields, including economics, biology, and engineering sciences.

Let’s learn how to write the WEIBULL function ourselves in Google Sheets and later test out the function with actual sample values.

 

 

The Anatomy of the WEIBULL Function

The syntax of the WEIBULL function is as follows:

=WEIBULL(x, shape, scale, cumulative)

Let’s dissect this formula and understand what each of these terms means:

  • = the equal sign is how we start any function in Google Sheets.
  • WEIBULL() is our WEIBULL function. It computes the value in a certain Weibull distribution given an input.
  • x refers to the input of our Weibull distribution function.
  • shape refers to the shape parameter of the Weibull function. It is usually denoted by the letter k or alpha in mathematics.
  • scale refers to the scale parameter of the Weibull function. We usually refer to it as lambda or beta in mathematics.
  • cumulative controls whether or not the WEIBULL function uses the cumulative or probability density function.
  • Both shape and scale must be greater than 0.

 

 

A Real Example of Using WEIBULL Function

Let’s look at a real example of the WEIBULL function being used in a Google Sheets spreadsheet.

In the example below, we were able to plot three types of Weibull distributions. 

The first distribution has a steep decline and trails off to the right. The second distribution in red closely resembles the normal distribution. The third distribution in yellow is slightly skewed to the left with its longer left tail.

Using WEIBULL Function in Google Sheets

 

To get the values in Column A, we just need to use the following formula in cell B4 and fill out the rest of the column:

=WEIBULL($A4,B$1,B$2,FALSE)

You can take a look at the formulas of the other distributions by checking out the sheet itself. You can make your own copy of the spreadsheet above using the link attached below. 

If you’re ready to try out the WEIBULL function in Google Sheets, let’s begin writing it ourselves!

 

 

How to Use WEIBULL Function in Google Sheets

This section will guide you through each step needed to start using the WEIBULL function in Google Sheets. 

Earlier, we discussed a scenario where you can use the Weibull distribution to determine laptop reliability. In this guide, we’ll use the WEIBULL function to determine how likely it is for our laptops to still be reliable after 5000 hours.

  1. First, we must add our values for alpha and beta into our spreadsheet.
    we need scale and shape arguments for our WEIBULL Function in Google Sheets
  2. Next, we simply have to indicate which function to use. To start our function, we can type out ‘=WEIBULL(‘ into the formula bar.
  3. Completing the function name will prompt a tooltip box to appear. You can minimize the tooltip box by clicking on the arrow seen on the top-right-hand corner of the box.
    type WEIBULL function into the formula bar
  4. The next step is to type in our arguments. For the first argument, we select the corresponding time duration in column A. The second and third arguments are the alpha and beta values. The fourth argument is set to TRUE since we want a cumulative probability.
    Afterward, simply hit Enter key on your keyboard to let the function evaluate.
    add arguments to weibull function
  5. Drag the formula down to fill out the rest of the column.
    fill out the survival probability with WEIBULL Function in Google Sheets
  6. To get the reliability, we simply have to subtract the values in column B from 1.
    Subtract probability from 1 to get the reliability
  7. We can convert the decimals into percentages for easier reading. The model tells us that there is a 94% chance that the laptop is still working after 5000 hours.
    convert probabilities into percentages
  8. Plot the table to have a better understanding of your data. From the chart, you can see that after the initial 5000 hours, the reliability of our product decreases at a rapid rate.
    Plotting WEIBULL Function

 

 

That’s all you need to remember to start using the WEIBULL function in Google Sheets. This step-by-step guide shows how easy it is to use the Weibull distribution to model various phenomena, including life data and product reliability.

The WEIBULL function is just one example of a mathematical function you can find in Google Sheets. With so many other Google Sheets functions out there, there are certain functions that can help you create more powerful worksheets.

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