A Power Transformation for Non-Normal Processes Capability Estimation

Abstract

The capability of a process is its ability to produce products that meet predefined requirements in industry and it is measured by capability indices. If data are not normally distributed, other techniques for capability estimation should be taken into consideration. One of frequently used methods are transformations to normal data distribution like Abbasi-Niaki, Box-Cox and Johnson transformation. In this paper, we propose modified power transformation method for non-normal process capability estimation. Proposed method is compared to Box-Cox, Johnson and Abbasi-Niaki transformation method using simulation studies under several theoretical non-normal distributions. Proposed modified transformation method finds optimal power to reduce data skewness in case of negatively and positively skewed data. In case the optimal power is not found, power to achieve minimal skewness is estimated. In case of negatively skewed data, algorithm transforms data to positively skewed. After applying each transformation, capability indices were estimated and then compared with theoretical indices by calculating relative bias. Proposed transformation method showed better performance than other methods in reducing skewness of negatively and positively skewed data. Study showed that performance of the proposed power transformation method was either better or comparable in estimating capability indices.