Building metamodels for quantile-based measures using sectioning

Simulation metamodeling has been used as an effective tool in predicting the mean performance of complex systems, reducing the computational burden of costly and time-consuming simulation runs. One of the successful metamodeling techniques developed is the recently proposed stochastic kriging. However, standard stochastic kriging is confined to the case where the sample averages and sample variances of the simulation outputs at design points are the main building blocks for creating a metamodel. In this paper, we show that if each simulation output is further comprised of i.i.d. observations, then it is possible to extend the original framework into a more general one. Such a generalization enables us to utilize estimation methods including sectioning for obtaining point and interval estimates in constructing stochastic kriging metamodels for performance measures such as quantiles and tail conditional expectations. We demonstrate the superior performance of stochastic kriging metamodels under the generalized framework through some examples.