  Stochastic kriging is a popular metamodeling technique for representing the
unknown response surface of a simulation model. However, the simulation model
may be inadequate in the sense that there may be a non-negligible discrepancy
between it and the real system of interest. Failing to account for the model
discrepancy may conceivably result in erroneous prediction of the real system's
performance and mislead the decision-making process. This paper proposes a
metamodel that extends stochastic kriging to incorporate the model discrepancy.
Both the simulation outputs and the real data are used to characterize the
model discrepancy. The proposed metamodel can provably enhance the prediction
of the real system's performance. We derive general results for experiment
design and analysis, and demonstrate the advantage of the proposed metamodel
relative to competing methods. Finally, we study the effect of Common Random
Numbers (CRN). The use of CRN is well known to be detrimental to the prediction
accuracy of stochastic kriging in general. By contrast, we show that the effect
of CRN in the new context is substantially more complex. The use of CRN can be
either detrimental or beneficial depending on the interplay between the
magnitude of the observation errors and other parameters involved.
