A known challenge in decision-based manufacturing of ceramics is that there are input uncertainties from data, models and model parameters. In a decision-based manufacturing environment, it is critical to know the probability that a ceramic will have a flexural strength below an acceptable limit. Regarding the flexural strength of silicon carbide (α-SiC), an absolute error bound of ±15% was set as a baseline previously in literature. However, this is inadequate because the uncertainty can shift both in its mean and standard deviation due to manufacturing-caused changes in microstructure and porosity. A Bayesian-based approach is proposed to dynamically and precisely provide a live uncertainty quantification (UQ) in a smart manufacturing environment. Five scenarios with variably perturbed flexural strength data are demonstrated. Across the scenarios the goodness-of-fit to the mean, as measured by R^2, is improved by a range from 0.12-0.61. Also, uncertainty is reduced from ±15% to ±12-±8% depending upon scenario.