Measuring PPM non-conformities for processes with asymmetric tolerances

Process yield has been the most basic and common criterion used in the manufacturing industry for evaluating process capability. The C_pk index has been used widely in the manufacturing industry. In this note, we considered a generalization of C_pk 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 C_pk index values and ratios of the two-side tolerances.