Hello,
I would like to revisit the discussion on non-normal control charts, which has already been addressed here.
https://community.jmp.com/t5/Discussions/Control-Chart-builder-Non-Normal-data-Control-Limits/m-p/227165#M45073
I also have a non-normally distributed data set (see attachment) for which only the SHASH distribution comes into question due to the extreme "skewness". All other distributions are rejected due to a significant goodness of fit test. However, using the Non-normal Control Chart script by Paul Deen (see link above, very helpful script by the way!) and selecting the SHASH distribution, a very questionable graph is displayed (zones too large for sigma boundaries), which is certainly due to the extreme skewness of the data (if you want to recap, my LSL is 0.9, my goal is to maximize)
If, on the other hand, I select a Weilbull distribution, the ControlChart looks much better.
Corresponding tests (Western Electric Rules) can then also be applied more reliably. My question now is whether it is acceptable to assume a different distribution for the creation of the control chart, although this is actually rejected via the goodness of fit test? I have also heard that a SHASH distribution in particular is not appropriate for process analyses (capability, control charts).
On the subject of data transformation: I have also tried to normalise the data using box-cox transformation (using the script from Mark Bailey, https://community.jmp.com/t5/JMP-Scripts/Demonstrate-the-Univariate-Box-Cox-Transform/ta-p/21820), but with little success. The data are simply too " skewed ". In addition I also found that transforming data is not that recommended as you loose certain information (see also https://www.spcforexcel.com/knowledge/variable-control-charts/control-charts-and-non-normal-data)
Do you have an opinion on this?
I would be very happy for any feedback!
Best regards
Johann
