Exact analytic expressions are given to evaluate the reliability of systems consisting of components, connected in parallel or series, subject to imprecise failure distributions. We also proposed a simplified version of the first order reliability method to deal with imprecision. This development allows engineers to evaluate the reliability of systems without having to resort to optimisation techniques and/or Monte Carlo simulation. In addition, this framework does not need to assume a distribution for the epistemic uncertainty, which permits a robust analysis even with limited data. In this way, the approach removes a significant barrier to the modelling of epistemic uncertainties in industrial probabilistic safety analysis workflows.