This paper compares the performances of Gini Mean, Clements and Box- Cox transformation methods for estimating process capability Indices when the distribution of the process data is (skewed) non-normal. The use of Process Performance Index (PPI) is implored for process capability analysis (PCA) using Weibull distribution. Simulation of data was also carried out using R software using a decision interval (target point) of 1.0 and 1.5. Performance assessment was carried out using Boxplots, descriptive statistics and the root mean square deviation. The following were the findings from the results. The Gini mean difference based process capability indices performs best in estimating the process capability indices closest to a set target for varying distribution parameters at different sample sizes, followed by Clements and lastly, the Box-Cox transformation method [10, 19].