In this paper we survey and critically comment on some basic concepts and notions relevant to the methodology dealing with process capability indices (PCI's). The emphasis is on distributional and inferential aspects. The intent is to contribute to the understanding and interpretation of these indices, if one is (unfortunately) required to use them. We regard them primarily as indicators of the expected proportion of nonconforming items, and not as having some relationship to arbitrary loss functions, as is currently the more fashionable viewpoint. New PCI's, related to the expected proportion of nonconforming items, are suggested.