The use of simulation-based uncertainty propagation approaches (e.g., Monte Carlo simulation method) can be computationally expensive if evaluating the function requires a relatively large computation time. To reduce the computation time, uncertainty propagation methods that use surrogate models (e.g., the Kriging method) may be used. In this paper, we extend the Kriging method to propagate the uncertainties from multiple sources, and for cases where the distribution of the prediction is produced at each trial (replication) of the simulation-based uncertainty propagation approach (i.e., at each sample point). The outputs of the methodology are the approximate percentiles of the output distribution. The capability of the methodology is tested using a Case Study involving the transport of solid particles in pipelines to prevent solid particle deposition and improve pipeline efficiency. Statistical comparisons suggest that our methodology successfully replicates the outputs from the Monte Carlo simulation method with a 94% reduction in computational cost. (C) 2016 Elsevier Ltd. All rights reserved.