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Reliability quantifies the ability of a system to perform its required function under stated conditions. The reliability of a decision is usually represented as the probability of an adequate functioning of the system where both the decision and uncontrollable variables are subject to uncertainty. In this paper we extend previous work on probabilistic constraint programming to compute such reliability, assuming probability distributions for the uncertain values. Usually this computation is very hard and requires a number of approximations, thus the computed value may be far from the exact one. Traditional methods do not provide any guarantees with respect to correctness of the results provided. We guarantee the computation of safe bounds for the reliability of a decision, which is of major relevance for problems dealing with non-linear constraints.