The transform yields an ad-hoc capability index it was not calculated objectively, instead it was optimized in a way that only benefits us as the producers. Therefore the acquired capability index will automatically be improved by a mathematical trick, rather than by any real reflection of the intrinsic process.
![minitab 18 nonnormal cpk minitab 18 nonnormal cpk](https://blog.minitab.com/hubfs/Imported_Blog_Media/image010.jpg)
The problem with normality transforms (like Box-Cox) is that they tend to camouflage outlying data points (those that otherwise inflate our capability indices) by "hiding" them into the bulk of the other data points. The purpose of a capability analysis is to provide the customer with evidence that the process/production we run for him/her is running reliably and within specifications. Power (e.g., Box-Cox) transforming data for capability analysis (and control charting) is a contentious issue. If you can provide more information on the nature of the process and the characteristic in quetions, we may be able to comment on the expected distribution. In summary, check the obvious causes such as out-of-control, but do not think that a non-normal process is always caused by that. Screw machines were a classic example of this situation. A process that uses a physical stop to control a dimension will typically have a non-normal distribution because you cannot get a dimension past the stop, but you can get any dimension short of the stop. Therefore, the closer you approach zero, the more non-normal the process will typically appear, while flatness distributions situated at a distance from zero may appear quite normal. You cannot have a parallelism or flatness less than zero. Some good examples of this are characteristics with a boundary condition (physical limit) such as zero. However, some processes are inherently non-normal. Some processes may indeed be non-normal because the process is out-of-control. I wanted to comment on the first paragraph.
![minitab 18 nonnormal cpk minitab 18 nonnormal cpk](https://1.bp.blogspot.com/-ONF4K-JBb8o/YH1rgv9rKAI/AAAAAAAAFYQ/MACaY2U4KNY0d2unU9ZWCzY1DuGxb24AQCLcBGAsYHQ/s386/Process%2BCapability%2BReport%2Bfor%2BYield%2B%28Kg%29.png)
![minitab 18 nonnormal cpk minitab 18 nonnormal cpk](https://blog.minitab.com/hubfs/Imported_Blog_Media/normal_capability_4.png)
Pabloquintana is correct about the two options.