Comparative study of response surface designs with errors-in-variables model

Abstract

This paper investigates the scaled prediction variances in the errors-in-variables model and compares the performance with those in classic model of response surface designs for three factors. The ordinary least squares estimators of regression coefficients are derived from a second-order response surface model with errors in variables. Three performance criteria are proposed. The first is the difference between the empirical mean of maximum value of scaled prediction variance with errors and the maximum value of scaled prediction variance without errors. The second is the mean squared deviation from the mean of simulated maximum scaled prediction variance with errors. The last performance measure is the mean squared scaled prediction variance change with and without errors. In the simulations, 1 000 random samples were performed following three factors with 20 experimental runs for central composite designs and 15 for Box-Behnken design. The independent variables are coded variables in these designs. Comparative results show that for the low level errors in variables, central composite face-centered design is optimal; otherwise, Box-Behnken design has a relatively better performance.