This paper identifies two correlation-based strategies for designing a simulation experiment to estimate a second-order metamodel of the relationship between the levels of the input factors and the response of interest. Both strategies are shown to be superior to the method of independent random number streams. In the past, correlation-based strategies for metamodel estimation in simulation experiments has focused on first-order metamodels. However, in many simulation experiments it is reasonable to expect that the relationship between the levels of the input factors and the response of interest is better approximated by a second-order metarnodel. Thus second- order metamodels are, typically, of more interest to the simulation analyst. Both proposed strategies use the variance reduction technique of common random numbers to induce positive correlations between responses across design points and antithetic variates across replicates. For a large class of experimental designs and with respect to a variety of optimality criteria, both strategies are shown to give better estimates of the vector of unknown coefficients in the metarnodel than the method of independent random number streams across all design points. A numerical example is given to illustrate this point and to show that in practice, the second strategy yields better metamodel estimates than the first strategy.
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