Box-cox transformation approach for evaluating non-normal processes capability based on the C_pk index

In manufacturing quality control and operations management, the process yield plays an important role. The capability index C_pk provides a lower bound on the process yield under the assumption that the process characteristic is normally distributed. When the normality assumption is violated, we can transform the non-normal data into normal data by using an appropriate transformation approach. In this paper, we consider the Box-Cox transformation and compare two estimation methods including the maximum likelihood estimator (MLE) and the method of percentiles (MOP). The performance comparison is based on the coverage rate, the precision, and the accuracy of the process non-conformity percentage evaluation. For various sample sizes and various distributions, several figures are presented to compare these two methods.