Stat 567:Statistical Reliability

Using Weibull Residuals
JMP Statistical Software


We show how to calculate Weibull residuals using the single fiber data. We will look one by one at how the appropriate columns were calculated.

The Residual column was calculated as follows:

From the output below, you can see that the numbers in the formula above are the MLEs in a Weibull regression with linear length effect.

Now we look at how the exponential residual column was calculated:

If the Weibull regression model fits, this column should have a Weibull Distribution with slope one. We check this using a Weibull plot:

As we can see this model does not seem to fit the data well. Let's try to add a quadratic length effect to the Weibull regression.

With this information we calculate another residual column

This residuals indicate a better fit but we are not there yet.

Another residual plot of interest is the following:

This plot indicates that we have removed the effect of length from these residuals.


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