Deterministic requirements are often used to express criteria for system properties such as system safety. However, the evidence presented to meet these requirements or targets is often uncertain, embodying both a lack of detail and inherent variability. Consequently it is difficult to establish definitively that these requirements have been satisfied. This paper presents a Bayesian approach that provides a framework for consideration of the ‘epistemic’ uncertainty (lack of knowledge) together with the ‘aleatory’ uncertainty (random variability) in system and component estimates. The ‘classical’ statistical approach is presented for some common scenarios each followed by the tool-assisted Bayesian inference approach. Finally, an example is presented of the uncertainties in the individual steps of an accident sequence that accumulate to the uncertainty in the likelihood of the accident itself. The main finding is that the use of a Bayesian inference tool such as OpenBUGS (Lunn et al. 2009) based on Markov Chain Monte Carlo (MCMC) techniques (Gelfand and Smith 1990) enables the burden of the computation to be lifted so that the engineer can then concentrate on the interpretation of the uncertainty in relation to the requirement.