Correlated Simulation Experiments in First-Order Response Surface Design

The collection of mathematical models, experimental strategies, and statistical inference referred to as response surface methodology (RSM) has been used in the empirical exploration of a wide variety of systems, particularly industrial situations in which a large number of variables influence the system response of interest. This paper examines experimental strategies for implementing RSM procedures in a simulation environment. Of particular interest is the question of how to best assign the pseudorandom number streams that drive the simulation to the experimental points when the objective is to estimate a first-order response surface model. We present general results for factorial and fractional-factorial plans where each factor is present at two levels. For this class of response surface designs, we consider three strategies for the assignment of pseudorandom number streams to experimental points: (i) the use of a unique set of streams at each design point; (ii) the assignment of a common set of streams to all experiments; and (iii) the simultaneous use of common and antithetic stream sets by the use of design blocking. We base our analysis of these correlation induction strategies on variance criteria commonly employed in response surface design, including: generalized variance, prediction variance, integrated variance, and variance of slopes. Our findings show that the simultaneous use of common and antithetic stream sets is the preferred correlation induction strategy, but that no one assignment procedure is uniformly superior for all four criteria. Our results provide a basis for selecting among the three correlation induction strategies.