Process capability indices are widely used in various industries as a statistical measure to assess how well a process meets a predetermined level of production tolerance. In this paper, we propose new confidence intervals for the ratio and difference of two C_pmk indices, based on the asymptotic and parametric bootstrap approaches. We compare the performance of our proposed methods with generalized confidence intervals in term of coverage probability and average length via a simulation study. Our simulation results show the merits of our proposed methods.