Experimental investigations of estimated response surface functions with different variability measures. (15th December 2009) - Goethals, Paul; Aragon, Lucy; Cho, Byung Rae
The primary goal of robust design is to determine the optimum operating conditions which minimise the variability of system performance and the deviation of the performance from its ideal target value. Response surface methodology (RSM), which is a key statistical method in modelling robust design, explores the functional relationship between several explanatory factors and a response variable. Our literature study indicates that three different estimators for variability measure, such as standard deviation, variance and the logarithmic transformation of standard deviation, are typically used; however, depending on which estimator is selected, different sets of optimum operating conditions are obtained which can further complicate comparison studies and data analysis. This question has not been addressed adequately in the robust design research community. This paper investigates how the selection of the three different estimators of variability affects optimal operating conditions in the context of response surface designs. The nominal-the-best quality characteristic is used to facilitate this experiment and numerical examples are provided to illustrate the findings.