The index C pmk combines the merits of the three earlier indices C p , C pk , C pm and alerts the user if the process variance increases and/or the process mean deviates from its target value. In practice, treat the calculated estimate C ˆ pmk as true value and ignore the effect on asymmetric tolerances may lead to misinterpretation of process capability. Pearn et al. [Pearn, W. L., Chen, K. S. & Lin, P. C. (1999). On the generalizations of the capability index C pmk for asymmetric tolerances. Far East Journal of Theoretical Statistics, 3(1), 47–66.] introduced a generalization of C pmk , which referred to as C pmk ″ , to handle processes with asymmetric tolerances. However, the sampling distribution of the estimator C ˆ pmk ″ is exceedingly complex and the derivation of an interval estimation of C ˆ pmk ″ is mathematically intractable. In this paper, we reformulate the explicit formulas and propose a heuristic algorithm to compute a lower confidence bound on C pmk ″ , which presents a measure on the minimum capability of the process, to enhance the applicability of the theoretical results. Tables are provided to assist the practitioners for a wide range of real world situation involving processes capability analysis. Equations and tables to estimate approximate sample size necessary to achieve a desired confidence limit with a specified confidence level are also developed. An application example on the trench capacitor etch process is also presented for illustrating the applicability of the generalization.