You could go a couple of different routes:
1) Perhaps the specification limits are unreasonable for a hand-made part. Engineers have been known to make these types of mistakes, regardless of their comments to the contrary.
2) The tools being used, or the level of skill of the person performing the duties is inadequate.
If you could expand on the problem (process, results, etc.) maybe some more light could be shed on the subject.
Keep in mind that process capability is just the measurement of a process as compared to the specification limits. It doesn't necessarily have anything to do with the actual quality of the end product.
Wayne