I'm very new to statistics and ran into a problem that I don't know the answer to. I want to do a capability analysis, but my data set is not normally distributed, so I transformed it using the Johnson transform in Minitab. Now I had a normal distribution and very good CP, CPK values. However, when I also approximated another function to the original data, the values of CP,CPK were lower by a factor of 10.

Now my question is how accurate is the Johnson transform. When can I use them and when not? My P-value was always well above 0.05 for the approximation and transformation. The size of the data set is n=40.

I would say the approximation is way better than the transformation to describe the process capability of the data, but I can't say why.

left: original dataset

middle: transformed dataset (CP= 1,78)

right: Approximation of a Weibull function to the original dataset (CP= 0,88)

(Lower and upper spec should be the same for approxiamtion and transformation, if i havent done a mistake there)

Maybe you can help me with that.

Thank you very much

Leon