First...Wellcome to the cove.
The cpk does not explain that issue.
The Cpk just evaluate the variation against the specs and make a penalty for not being the center to them.
The Cpk it self doesn't tell how many samples where taken, the sample size could make the
cpk estimate :mg: have large or small confidence interval. As I said in other post is better to use Cpk minimum estimated value so you can compare the Cpk form different sample sizes correctly (or establish a minimum of 100 samples for example)
How can be answered "
is the process stable?", is not clear, there are two (at least) phylosofies.
1- Not presenting any pattern on the control chart (well maybe 2 in a 100 sample could be considered stable). The issue here is wich patten apply to your process, not every GE rule applies to any process.
2- I found scarse information about this other one but IMHO the right way. take SPC as statistical hypotesis testing (to compare mean and variation with a "t" and an "F" test) from one period of time to the other (use 90% confidence tables because is not a controlled experiment). The root on this is that if you have the same mean and the same variation, the process could be predicted.
Try to read this... (is not publicity but thanks to Donald Wheeler's SPC Press and their reading room), it's a MUST.
A change in terminology