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This study investigated the effect on simulation output of repeatedly sampling an embedded metamodel. A metamodel is said to be embedded within a simulation if it is used to replace a submodule of that simulation. Replacing a deterministic module with an embedded deterministic metamodel poses no apparent mathematical problems. However, using a deterministic metamodel to replace a stochastic simulation component could require additional corrective actions. This research was performed in two phases. The first phase dealt with a set of tandem queues. It was shown that as each queue was sequentially replaced with a metamodel, the total system variance was inappropriately diminished. A theoretical model of the error components was postulated and used to compensate for this missing variation, restoring the parent simulation's variance to approximately its original level. In the second phase, the problem was extended to the case of repeatedly sampling an embedded metamodel with similar results. In addition, guidelines for metamodel use were presented. In some situations, sampling from a probability distribution is more appropriate than the use of metamodel. (AN)

This study investigated the effect on simulation output of repeatedly sampling an embedded metamodel. A metamodel is said to be embedded within a simulation if it is used to replace a submodule of that simulation. Replacing a deterministic module with an embedded deterministic metamodel poses no apparent mathematical problems. However, using a deterministic metamodel to replace a stochastic simulation component could require additional corrective actions. This research was performed in two phases. The first phase dealt with a set of tandem queues. It was shown that as each queue was sequentially replaced with a metamodel, the total system variance was inappropriately diminished. A theoretical model of the error components was postulated and used to compensate for this missing variation, restoring the parent simulation's variance to approximately its original level. In the second phase, the problem was extended to the case of repeatedly sampling an embedded metamodel with similar results. In addition, guidelines for metamodel use were presented. In some situations, sampling from a probability distribution is more appropriate than the use of metamodel. (AN)

In the field of structural reliability, the Monte-Carlo estimator is considered as the reference probability estimator. However, it is still untractable for real engineering cases since it requires a high number of runs of the model. In order to reduce the number of computer experiments, many other approaches known as reliability methods have been proposed. A certain approach consists in replacing the original experiment by a surrogate which is much faster to evaluate. Nevertheless, it is often difficult (or even impossible) to quantify the error made by this substitution. In this paper an alternative approach is developed. It takes advantage of the kriging meta-modeling and importance sampling techniques. The proposed alternative estimator is finally applied to a finite element based structural reliability analysis.

This research investigated the combined influence of simulation work and metamodel specification on the statistical quality of the estimates obtained from the resulting metamodels of the simulation data. A 9 x 2 x 2 experiment consisting of 9 cases of simulation work, 2 levels of metamodel specification, and 2 levels of design fractionation were designed for 8 different configurations of M/M/k queues. The only observed statistic for this experiment was the average queue length. Simulation estimates for each configuration's average queue length were calculated directly from the simulation data. In addition, the metamodels were fit to the simulation data and were used to estimate the average queue length for each configuration. Residuals were calculated for each estimate as the difference between the analytic solution for average queue length and the given estimate. The residuals were analyzed graphically and via Single-Factor ANOVA to determine if the amount of simulation work or metamodel specification affected the statistical quality of the estimates. This research showed conclusively that the amount of simulation work had no significant effect and that the metamodel specification had a significant effect on the statistical quality of the estimates obtained from metamodels. Response surface methodology, Computer simulation, Least squares regression, Experimental design, Metamodel, M/M/k Queues.