Pearn and Chen (1997) proposed a class of capability indices _Np (u, v) which generalize the process capability indices C_p (u, v)(Vnnman, 1995) to accommodate cases where the underlying distributions may not be normal. The current indices _Np (u, v) are functions of quantiles which may not be known. In this article, we apply some existing quantile estimators to estimate the class of indices C_Np (u, v). It is shown that the estimators of _Np (u, v) we propose are all asymptotically normally distributed and equivalent and can perform better than the estimated C_p (u, v) in some instances.