Greenwich and Jahr-Schaffrath (1995) introduced an index C-pp, a simpl
e transformation of the index C(pm), which provides an uncontaminated
separation between information concerning the process accuracy and pr
ocess precision. Unfortunately, the index C-pp inconsistently measures
process capability in many cases and thus reflects process potential
and performance inaccurately. In this paper, we consider a generalizat
ion, C ''(pp), to handle processes with asymmetric tolerances. The gen
eralization is shown to be superior to the original index C-pp. In add
ition, we investigate the statistical properties of a natural estimato
r of C ''(pp) assuming the process is normally distributed.