On the use of data transformation in response surface methodology

摘要

One of the main objectives of response surface methodology is to find the operating settings that optimize the mean function. When estimating the optimum settings, it is highly important to take the response variance into account. Data transformations are frequently used to eliminate variance heterogeneity. Important references in response surface methodology such as Box and Draper and Myers et al recommend transforming the data prior to process optimization, if needed. Process optimization is initialized if the response transformation successfully stabilizes the variance. In this paper, I oppose using such a practice without complete understanding of its implications. It basically implies that variation is a key characteristic of the process understudy and postulates relationship between the mean and the variance. When ignoring this relationship, the optimum settings found on the transformed scale may have very high variance. A solution based on ridge analysis is presented. Practitioners must proceed with caution when applying data transformation to their datasets.