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Assessment of reliability and safety of a complex system with sequential failures is an important issue in industries, since the reliability and safety of a complex system depends, not only upon all failed states of the system components, but also upon the sequence of occurrence of those failures. In this paper, we present an alternative methodology for assessing sequential failures in a complex system. In previous research, the probability of sequential failures is computed based on tracking the markings of Petri net models and it is assumed that the time to failure of basic events follows an exponential distribution. To overcome the limitations of the current methods in applying Petri nets for assessment of sequential failures, the method presented in this paper employs the concept of counters used in Petri net simulation to perform sequential failure analysis and is developed based on evolution equations that describe the dynamics of the system. It is demonstrated with a sequential failure analysis example of an automated machining and assembly system.