This paper presents a method for evaluating the probability of catastrophic failures in process systems. A Markov model is applied that takes into account dynamic phenomena of the safety-system components failure and repair, as well as those of the physical process. An approximate solution method reducing the computational time and memory requirements is presented. The method is demonstrated through a two-compressor refrigeration system serving an ammonia storage tank. The results are compared to those of the full Markov model and of the classical fault tree analysis. (C) 2003 Elsevier Ltd. All rights reserved.