Process capability analysis is an effective and efficient tool for quality assurance. When the distribution of the underlying quality characteristics is not normal, modifications of the basic process capability indices are required. Literature in process control provides avenues to resolve the issue of non-normality and data transformation is one of the approaches frequently applied in practice. Primarily the Box – Cox transformation (BCT) is employed to transform the non normal data into normal data which originally utilizes the method of maximum likelihood estimation (MLE) to find the single transformation parameter λ. There are alternative methods to estimate the optimal parametric value λ using goodness of fit tests rather using MLE method. In order to bring improved estimates, this paper makes a fresh attempt to estimate process capability analysis (PCA) using transformed data through different goodness of fit tests. The simulation study uses variety of asymmetric behaviors from a Weibull distribution generating a random sample of 100 data points to find the best goodness of fit test for better process capability estimates that are compared to the standard of six sigma results for non-normal data. Final result shows that Shapiro-Wilk's (SW) and Artificial Covariate (AC) methods are performing well when compared to the method of MLE. Minitab software and R programming language were utilized for data simulation and analysis.