Summary: M. Greenwich and B. L. Jahr-Schaffrath [Int. J. Qual. Reliab. Management 12, 58-71 (1995)] introduced an index \(C_{pp}\), a simple transformation of the index \(C^*_{pm}\), which provides an uncontaminated separation between information concerning the process accuracy and process precision. Unfortunately, the index \(C_{pp}\) inconsistently measures process capability in many cases and thus reflects process potential and performance inaccurately. We consider a generalization, \(C_{pp}'\), to handle processes with asymmetric tolerances. The generalization is shown to be superior to the original index \(C_{pp}\). In addition, we investigate the statistical properties of a natural estimator of \(C_{pp}'\) assuming the process is normally distributed.