How to Plot Weibull Distribution in Excel (with Easy Steps)

The Weibull Distribution is a continuous probability distribution that is used to analyze life data, model failure times, and assess the reliability of access products.  This distribution is used in different fields to analyze data.

Reliability Function: R(t) = e^-[{(t-γ)/α}^β]

Where,
β = Shape Parameter.
α = Scale Parameter.
γ = Location Parameter, which is usually 0.
From R(t), we can calculate the Failure function F(t):

F(t) = 1-R(t)

After calculation, we get
ln(ln(1/(1-F(t))) = βlnt-βlnα
This resembles the y=mx+c equation

Consider the following dataset, containing instances of failure and the number of days of the failure. For example, the 1st failure occurs after 400 days, 2nd one after 820 days, etc.

Let’s use this data to calculate the Weibull Distribution and understand the failure rate.

Step 1 – Calculate Median Rank

To calculate the median rank we will use Bernard’s approximation.

• Go to cell D5 and enter the following formula:

• Press ENTER to get the output.

• Use the Fill Handle to AutoFill up to D14.

Step 2 – Determine Natural Logarithm

Now we can calculate the natural logarithm. First, we will determine the logarithm of days.

• Go to E5 and enter the following formula:

• Press ENTER to get the output.

• Use Fill Handle to AutoFill up to E14.

• In a similar way, we will fill up the next column. The formula in F5 will be:

• Press ENTER to get the output.

• Use the Fill Handle to AutoFill up to F14.

Step 3 – Plot Distribution Chart

Now we can plot a chart using ln(days) as x-axis and ln(ln(1/(1-F(t)))) as y-axis.

• Select E4:F14.

• Go to the Insert tab.
• Select the Scatter option.
• Select one you like.

Excel will create a scatter plot.

• Rename the plot to Weibull Distribution.

Read More: How to Create a Distribution Chart in Excel

Step 4 – Compare Equation to Determine Coefficients

Now we will determine the parameters. We will derive the trendline equation and compare it with the equation ln(ln(1/(1-F(t))) = βlnt-βlnα

• Go to Chart Design.
• Select Add Chart Element.
• Select a Trendline.

Excel will add a trendline.

• Select the trendline and right-click your mouse.
• Select Format Trendline.

• Check the box for Display Equation on Chart.

Excel will display the equation.

• The equation is y=1.9551x-14.663. After comparing with ln(ln(1/(1-F(t))) = βlnt-βlnα, we get
  • β = 1.9551
  • βlnα = 14.663
• Using these values, we get
  • α = 1807.811

• So, the Reliability Function becomes

R(t) = e^-[(t/1807.811)^1.9551]

Things to Remember

The shape parameter indicates the failure rate:

• If β < 1, then the failure rate decreases with time
• If β = 1, then the failure rate is constant
• If β > 1, the failure rate increases with time

Use absolute references to lock a cell.

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• Plot Normal Distribution in Excel with Mean and Standard Deviation
• How to Plot Frequency Distribution in Excel
• How to Plot Poisson Distribution in Excel
• How to Plot Particle Size Distribution Curve in Excel
• How to Create a Probability Distribution Graph in Excel

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