Construction of Stochastic Simulation Metamodels based on Unreplicated Smoothed Data

Metamodels are used for the analysis and optimization of real systems. The construction of a metamodel requires, in order to collect meaningful statistical data, a number of replicated simulation runs executed at each design point. We propose spreading those replications to an equal set of new neighboring design points. The resulting experimental design includes a single replication at each design point. The information collected from the additional points is balanced by a lack of statistical information from each point. Using smoothing techniques, we propose building the missing statistical information at each design point using the neighbors as approximate replications. This can lead to a better adjustment with less simulation runs. Two statistical tests are used to safeguard the applicability of the proposed procedure. Some examples are used to illustrate the increase in efficiency and approximation of the proposed approach.