Censored data arise naturally in industrial experiments whose observations are failure times or measurements with mixed continuous-categorical outcomes. When censored data are observed from a fractionated experiment, likelihood-based estimates quite often do not exist, especially when the opportunity for improvement is great. To circumvent this problem, we propose a Bayesian analysis strategy that has a straightforward implementation using the data augmentation and Monte Carlo EM algorithms. For nonregular designs with complex aliasing patterns, a modified analysis strategy is proposed that substantially reduces the computation needed for model selection. The proposed strategy is illustrated using data from three real industrial experiments. For these data sets, the analysis results are fairly insensitive to the specification of the prior.