In many industries process capability studies are conducted in order to determine the capability of the process to produce acceptable products and it is one of the important activities of statistical process control. In order to express the capability of a process, process capability indices are frequently used. However, they are usually computed under the assumption that the process data follow a normal distribution. Normality assumption may be violated and the use of these traditional capability indices may cause misleading interpretation about the capability of the process. One of the most widely discussed methods to handle non-normality is Clements’ method which was proposed in 1989. Clements’ method uses the Pearson family of curves for calculating capability indices for any shape of distribution. It requires the estimation of the mean, standard deviation, skewness and kurtosis and makes use of the classical estimators of skewness and kurtosis. In this study, we discussed the use of more robust estimators of skewness and kurtosis in the calculation of process capability index by Clements’ method. For this purpose, capability indices with the use of these robust estimators are computed by simulation and the mean square errors of them are reported. The comparison is done through simulating Weibull and lognormal data with several different parameter values. Finally, a real life application to oil pump manufacturing in automotive industry is presented.