## Weibull Explained (a bit)

Adam / April 21, 2017

Many of our customers (internal/external) trust us when we say that a Weibull analysis is the best approach to understanding what the data set is telling us. We then take their data set, do something mysterious where no one can see us, and then present these accurate predictions as to what is going to happen with a given population of the product at some future date.

Yes, Weibull analysis in its entirety is complex, but the base principle is pretty simple, and even something we are all familiar with. I believe we can all recall being given two points on a graph and asked to derive the equation for the line that will capture those two points. We did this by finding the factors in the equation for a line.

- The equation is “y=mx+b”
- The line this equation creates crosses the y-axis at “b”
- It has a slope of “m”
- And for any given x coordinate “x”, it will have a y coordinate of “y”

So having derived this equation from these two points you can now “predict” other points along the line. If the “x” axis happened to be representative of time then you could predict where the line would be in the future by entering a larger “x” value.

And that is it! That is the basic principle of what a Weibull distribution is used for with a data set.

So why is Weibull so complex?

**1: No one gives you two data points. The last set I received had 47,000 data points**

So now you have to estimate what is going to be the “best fit” line to characterize that population.

**2: Ok if that is a “best fit” line then what is the range that I can be 90% confident the true line is within?**

Now we need to calculate confidence bounds.

**3: The data set is most likely not easily characterized as a straight line**

So obviously a line is not going to characterize all data sets. We need equations with more variables that can interact in a higher level of complexity to capture more complex behavior. Many exist, but Weibull is used often due to it’s dynamic ability to twist itself into almost any shape.

That’s why we data lovers so often pull our Weibull tools out of the toolbox when we need to find out what the data is trying to tell us and make a prediction.

Adam-

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