Data Transformations with a Full 2⁶ Experimental Design—A Metal-Cutting Case Study

ABSTRACT

The Box-Cox transformation was evaluated with reference to a six-factor full-factorial (2⁶) data set with 64 runs. The data were used to determine the optimal operating conditions for a milling machine with respect to surface finish. A suitable transformation was determined by minimizing the mean square errors, evaluating the size of the effect significances and the normal probability plots of the estimated effects, Shapiro-Wilk tests, and the model residuals. The achievement of both normality with constant variance and a simple model came about as a result of a trade-off between several different criteria.

KEYWORDS:

• Box-Cox transformations
• design of experiments
• expectations
• normal probability plot
• residuals

Notes

Bold values are statistically significant (p < 0.05).

Additional information

Notes on contributors

E. Mønness

Erik Mønness is Associate professor in Statistics and research advisor at Hedmark University College, Norway, and visiting professor at the Industrial Statistics Research Unit, University of Newcastle, UK. He has worked with applied statistics, especially with linear models and statistical software within health issues, agriculture, forestry and industry. He is Cand. Real. in mathematical statistics from University of Oslo 1976. He has also been President (Vice Chancellors) at Hedmark College, Visiting Scholar at Stanford University, Dean and later Vice President (Pro-Vice Chancellors) at Hedmark University College. He has also been member of the Research Advisory Group at the Norwegian Council for Higher Education.