Process yield has been the most basic and common criterion used in the manufacturing industry for evaluating process capability. The Cpk index has been used widely in the manufacturing industry. In this note, we considered a generalization of Cpk index which handles processes involving a target T with asymmetric tolerances. Particularly, we established a formula for measuring the PPM non-conformities for given ratios of the two-side tolerances. We proved the validity of the established formula and tabulated the upper bounds on PPM non-conformities for various given Cpk index values and ratios of the two-side tolerances.