Composite pressure vessels are indispensable when picturing a green hydrogen economy. The manufacturing process of these vessels introduces numerous material imperfections like voids, misaligned fibers, and fiber volume fraction variations. The presence of these variabilities leads to a highly stochastic vessel burst pressure. The authors develop an uncertainty quantification framework that predicts the burst pressure of composite pressure vessels. It accounts for spatial material variability of fiber misalignment, fiber volume fraction and fiber strength. The data needed for representing this material variability is obtained from measurements. Burst predictions are validated by comparing them to physical burst tests. A comparison shows that the framework predicts a burst pressure that is, on average, 5.8% lower than the experimental burst pressure. A subsequent sensitivity analysis quantifies the effect that several modeling hypotheses have on the predicted burst pressure. The results show that the prediction difference can mostly be explained by uncertainty on the identified fiber strength parameters, and the used fiber break model.