Summary: A recent, pioneering paper by S. Kocherlakota et al. [Int. J. Math. Stat. Sci. 1, No. 2, 175-209 (1992; Zbl 0792.62091)] seems to be the first attempt at exact determination of the distribution of the process capability indices \(\widehat{C}_p\) and \(\widehat{C}_{pk}\) for some nonnormal population distributions – namely those represented by (i) contaminated normal and (ii) Edgeworth series expression distributions. In this note a simpler derivation of results regarding (i) is presented, and they are extended to cases of three or more contaminated components.