Engineers use semi-empirical models of complex degradation phenomena to manage the integrity of structural systems. Historically, the intended application of these models has been to perform deterministic calculations to demonstrate that failure is not expected. However, as integrity management systems are increasingly optimised decision makers require quantified likelihoods of events such as failure to help ensure that maintenance investments are completed where and when they are worthwhile. In the probabilistic application of degradation models, inherent and un-quantified conservatism can lead to ineffective risk management. Bayesian analysis can be used to fit semi-empirical degradation models to existing test data (and can be updated if new data is available) such that the variability within, and the inter-dependency between all model parameters is quantified and accounted for. This includes model uncertainty parameters. In this report, an SN curve and a two-stage Paris Law model have been fitted using Markov Chain Monte Carlo sampling. The benefits and challenges associated with this approach are discussed in the context of existing standards and guidelines developed for industry. Posterior predictive sampling is used to demonstrate how the models can be used to produce results that are fully compatible with a Bayesian decision analysis.