I had some parts made recently that were formed on a press brake. There was one critical dimension, the width of an opening. The specification limits on the width of an opening was 3.13" to 3.19". The limits were decided as most of these things are by a long meeting.
The fabricator made an initial three items to tune the press brake settings. The opening width on the first three items was 3.1870, 3.1880, and 3.1745.
The opening width for the run on the successive items, produced after the press brake program was finalized, are as follows:
The mean on those items is 3.1792
and the standard deviation is .0068
We can now calculate the Cpk for the process. Cpk is given by (See the discussion here
Cpk= min(.52, 2.4)
Therefore, Cpk=.52. Another way of looking at this is a Cpk=0.5 gives 6.68% nonconforming fraction. This can be seen in the graph below.
Looking at the mean as opposed to the specification limits we see that the process is not centered within the specification limits. Given the process standard deviation we calculate what the process ought to be capable of doing.
We calculate Cp=1.47. This is pretty good.
Hmmm. A Cpk=.52 and Cp=1.47, it seems that all we need to do is center the process within the specification limits. A few words are in order now.
This was a small run. The fabricator had deliberately decentered the process with my knowledge. There were some other design features that the fabricator was worried about destroying if the opening was too narrow. So we opted to go wide. This resulted in having to inspect every item to ensure that the specification was met.
For a small run such as this it was not a hardship. For a really large run the optimal solution would have been to do some minor redesign to allow the process to run centered. This is a much more robust solution than inspecting each item for acceptability.
Finally, this data was not from a true capability study. I analyzed the data to satisfy my curiosity about the process capability. For a true study I would need to verify that the process was stable and check that the data is normally distributed.