Simulation designs and correlation induction for reducing second-order bias in first-order response surfaces

Construction of simulation designs for the estimation of response surface metamodels is often based on optimal design theory. Underlying such designs is the assumption that the postulated model provides the correct representation of the simulated response. As a result, the location of design points and the assignment of pseudorandom number streams to these experiments are determined through the minimization of some function of the covariance matrix of the model coefficient estimators. In contrast, the authors assume that the postulated model may be incorrect. Attention is therefore directed to the development of simulation designs that offer protection against the bias due to possible model misspecification as well as error variance. This particular situation examined is the estimation of first-order response surface models in the presence of polynomials of order two. Traditional two-level factorial plans combined with one of three pseudorandom number assignment strategies define the simulation designs. Specification of the factor settings for these experimental plans are based on two integrated mean squared error criteria of particular interest in response surface studies. For both design criteria, comparisons of the optimal designs across the three assignment strategies are presented to assist experimenters in the selection of an appropriate simulation design.