Process capability indices Cp(u, v), which include the four basic indices Cp, Cpk, Cpm and Cpmk as special cases, have been proposed to measure process potential and performance. Cp(u, v) are appropriate indices for processes with normal distributions, but have been shown to be inappropriate for processes with non-normal distributions. In this paper, we first consider two generalizations of Cp(u, v), which we refer to as CNp(u, v) and C′Np(u, v), to cover cases where the underlying distributions may not be normal. Comparisons between CNp(u, v) and C′Np(u, v) are provided. The results indicated that the generalizations CNp(u, v) are superior to C′Np(u, v) in measuring process capability. We then present a case study on an aluminum electrolytic-capacitor manufacturing process to illustrate how the generalizations CNp(u, v) may be applied to actual data collected from the factories.