Uncertainty quantification (UQ) is a framework used frequently in engineering analyses to understand how uncertainty in system inputs lead to uncertainty in the system output. An instability is observed in a UQ method proposed by Roy and Oberkampf and a Bayesian Markov Chain Monte Carlo approach to UQ is offered as an alternative. The Bayesian approach allows analysts to incorporate information from various available sources including observed measurements and expert opinion and to update the analysis and results as more information becomes available. An illustrative engineering example is provided as a platform to demonstrate the Bayesian UQ approach and to compare it with the Roy and Oberkampf method. Methods for visualizing and interpreting the results from the Bayesian UQ approach are explored. This research is expected to produce a new approach to UQ that will be useful to engineers and other practitioners as they quantify the uncertainty in a system, visualize the uncertainty, and interpret the results to inform decisions
