random selection of calibration experiments and the hold-out experiments 130 times. Therefore, a total of 1820 random estimates of forecasting errors are obtained. Figure 3 displays the results obtained as a result of this extensive simulation campaign. Figure 3: Forecasting errors as a function of number of experiments. Regarding this example, let’s say 50 psi is an acceptable forecasting error for a given application. Figure 3 illustrates that the sixth batch yields a forecasting error less than this allowable limit. To verify consistency, one or two more batches may be desirable. According to Figure 3, we can decide that a total of 6 batches, 24 experiments would be sufficient. At this stage, if a more stringent requirement must be imposed, say for instance a 25 psi threshold for the forecasting error, then additional experiments can be conducted until the forecasting errors are observed to be consistently lower than the allowable errors, which in our example corresponds to the 9th batch. For these allowable forecasting errors, certification of an engineering system can be successfully accomplished by conducting a significantly fewer number of experiments. 6 CONCLUSION Model-based certification heavily relies on simulation model solutions while determining the capacity of engineering systems. Several approaches to certification are proposed that depend on knowing the mean performance of the system. These methods lack a consideration of additional bias and uncertainty as a result of forecasting. However, certification would not be possible unless the forecasting 443
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