More specific and accurate probabilistic models of the numbers of fragments generated respectively by Boiling Liquid Expanding Vapor Explosions (BLEVEs), Mechanical Explosions (MEs), Confined Explosions (CEs), and Runaway Reactions (RRs) of a horizontal cylindrical vessel were developed using the maximum entropy principle based on historical accident data. The theoretical results from the four probability density functions were compared to the observed data, and the numbers of fragments followed discrete exponential distributions in the interval [1, 9]. Beside the summary of the probabilistic distributions of the other random variables in the process of fragment projection, the effects on the fragment trajectory and target terms were investigated using a parametric approach. The results showed that using the complete model, wind shear, turbulence, and absence of fragment rotation caused the fragments to impact within shorter distances; fragment rotation and lack of wind decreased the probability of impact within a given distance, but the rupture probability of the target was not affected by fragment rotation or wind. The probabilistic confidence intervals of fragment range, impact, and target penetration became narrower with the number of simulation runs, but the accuracy of the results increased. The probability of fragment impact increased with the volume of the target vessel and the degree of filling of the explosion vessel, but did not depend on the kind of explosion. The probability of target rupture increased slowly with the degree of filling of the explosion vessel, but was little influenced by the volume of the target vessel or the kind of explosion. (C) 2011 Published by Elsevier Ltd.