Miner is correct that Cpk came over from the Japanese in the mid 80s (Sullivan, L. P., "Reducing Variability: A New Approach to Quality", Quality Progress, July 1984)
The automotive industry unnecessarily complicated the original concept by introducing the concept of short and long term variation (Cpk & Ppk)
Steven is correct in that some Six Sigma folks started to corrupt Cpk with a bunch of nonsense about:

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if you are interested in the defect rate (for cost and yield impacts to delivery, or fro understanding the inspection needs) then you are far better off counting the number of defects that actually occur. (Pyzdek, Thomas, "Why Normal Distributions Aren't [All That Normal]", Quality Engineering 1995, 7(4), pp. 769-777)
If you are interested in the overall variation of the process in relation to the specifications, you are better off plotting the process results in a multi-vari chart and comparing to the specification limits. (it is insensible to reduce variation to a single number)
If you are interested in the future stability of the process you are better off plotting the process in a multi-vari and/or control chart and understanding the science then applying the appropriate controls to maintain stability and detect changes quickly. (statistics doesn't obviate science)
Cpk (and all of its illegitimate children) simply can't do any of the above for you...
The automotive industry unnecessarily complicated the original concept by introducing the concept of short and long term variation (Cpk & Ppk)
Steven is correct in that some Six Sigma folks started to corrupt Cpk with a bunch of nonsense about:
- being able to predict very low defect rates based on the tails of the Normal distribution
- espousing that the difference between the long term and short term capability represented the entitlement of the process; preaching that assignable causes are easy to eliminate and that common causes are not.
- and then came the 1.5 sigma shift abomination
- and then insisting that everyone had to have Cpk values for every characteristic or they weren't really 'doing' six sigma...

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if you are interested in the defect rate (for cost and yield impacts to delivery, or fro understanding the inspection needs) then you are far better off counting the number of defects that actually occur. (Pyzdek, Thomas, "Why Normal Distributions Aren't [All That Normal]", Quality Engineering 1995, 7(4), pp. 769-777)
If you are interested in the overall variation of the process in relation to the specifications, you are better off plotting the process results in a multi-vari chart and comparing to the specification limits. (it is insensible to reduce variation to a single number)
If you are interested in the future stability of the process you are better off plotting the process in a multi-vari and/or control chart and understanding the science then applying the appropriate controls to maintain stability and detect changes quickly. (statistics doesn't obviate science)
Cpk (and all of its illegitimate children) simply can't do any of the above for you...