Comparison between Nonnormal Process Capability Study Based on Two Kinds of Transformations

Standard process capability index is based on the assumption that process output obeys normal distribution. There exist a lot of process outputs which don´t obey normal distribution, such as F distribution, Γ distribution, χ² distribution, and β distribution. There are many ways to transform non-normal data to normal data, two of which are using the Box-Cox transformation and Johnson transformation. In this paper, some nonnormal distributions are studied by using these two transformations respectively, their process capability indexes are calculated, and the applicability and effectiveness of the two methods in process capability analysis are studied through a large number of repeated simulations. It is shown that Johnson transformation is more effective than Box-Cox transformation.