A method for calculating the dynamic reliability of safety systems and its application to a refrigerated liquid cryogenic ammonia storage tank is presented. The method is based on the theory of Markov chains and can model dynamic phenomena of the process and its safety systems. It offers the capability of modelling realistically the competing process of repairing failed safety systems and the exceeding of safe limits by some critical physical parameters of the process. The results of the Markovian analysis are compared to those of the classical Fault Tree/Event Tree methods and it is shown that the proposed method offers a substantial improvement over the classical approach. The probability of failure from overpressure of a cryogenic ammonia storage tank depends in general on the level of the ammonia in the tank at the time of accident initiation. Assuming a uniform distribution for the ammonia level in the tank, the average upper and lower limits for the failure probability over a year provided by the FT/ET methods span three orders of magnitude [1.4x10(-1)-1.0x10(-4)] depending on whether repair is considered or not. The proposed approach realistically determines this failure probability at 3.3x10(-3). Additional results from specific levels of ammonia are also provided. (C) 2000 Elsevier Science Ltd. All rights reserved.