A comparison of two methods for transforming non-normal manufacturing data

Abstract

Many statistical methods applied to manufacturing quality control and operations management have been under the assumption that the process characteristic investigated is normally distributed. If the process characteristic is not normally distributed, a popular approach is to transform the non-normal data into a normal one. In this paper, we consider the Box-Cox transformation, and compare the transformation power using two different parameter estimation methods, including the maximum likelihood estimator (MLE) and the method of percentiles (MOP). The performance comparison is based on the pass rate under the Shapiro-Wilk normality test. The results show that, in general, the MOP has better pass rate, while the MLE has smaller power variation for most cases investigated. For small sample size (n = 5, 10) both methods perform equally well. For large sample size, the MOP is recommended due to its simplicity and significantly higher pass rate.