The process capability index Cpk has been widely used in manufacturing
industry to provide numerical measures of process potential and performance. As noted by
many quality control researchers and practitioners, Cpk is yield-based and is independent
of the target T. This fails to account for process center ing with symmetr ic tolerances, and
presents an even greater problem with asymmetric tolerances. To overcome the problem,
several generalizations of Cpk have been proposed to handle processes with asymmetric
tolerances. Unfor tunately, these generalizations understate or overstate the process capability
in many cases, so reflect the process potential and performance inaccurately. In this
paper, we first introduce a new index C"pk , which is shown to be super ior to the existing
generalizations of Cpk . We then investigate the statistical properties of the natural estimator
of C"pk , assuming that the process is normally distr ibuted.
