Johnson transformations are used in a way similar to Box-Cox transformations. First, apply a transformation to the response, and then use the transformed data with a normal distribution to find capability.
As with using other distributions to fit to nonnormal data, we should investigate the reasons for our data being in the shape it is before attempting Johnson transformations. For more notes on what to look out for, see the Capability analysis for nonnormal distributions recipe.
The main benefit of Johnson transformations over Box-Cox transformations is the ability of the former to transform data with negative values or 0 values. They can also be useful in situations where a process or data set has an extreme boundary condition that makes other distributions difficult to fit to. One example of where this may be used is for breaking stresses.
As with the previous examples on nonnormal distributions and Box-Cox transformations, we will use the data...