Probabilistic risk analysts routinely encounter problems in which they are faced with non-trivial measurement errors, empirical data with very small sample sizes, uncertainty about the appropriate shape of the statistical distributions, unknown dependencies induced by common-cause or common-mode failures, and possibly doubt about the structural form of the model itself. Traditional applications of probability theory, often implemented by Monte Carlo simulation, have usually had to neglect these kinds of uncertainty, which leads of course to diminished credibility for the assessments. Approaches involving second-order Monte Carlo simulation, robust Bayes methods or the theory of imprecise probabilities have been suggested as computational tools to account for these uncertainties and assess the reliability of probabilistic risk analyses, but these approaches are generally computationally intensive and sometimes theoretically problematic. Probability bounds analysis is a marriage of probability theory and the techniques of interval analysis that generalizes and is faithful to both. By focusing on bounding the cumulative distribution functions characterizing the risk outputs, probability bounds analysis simplifies the treatment of imprecisely specified marginal distributions, poorly characterized (or completely unknown) dependencies and even some aspects of model uncertainty. This approach allows one to directly compute rigorous and often best-possible bounds on the probabilities of adverse events and thus provides estimates of the reliability of a probabilistic risk assessment. It allows analysts to give quantitative and comprehensive answers to the "are you sure?" questions about a probabilistic risk assessment.