Failure analysis with multiple failures and reliability assessment of complex systems is a very important task for many industries. The objective of the dissertation is to develop a new integrated approach for systems failure analysis and enhance the existing sequential failure analysis methods.; An extensive research is conducted to investigate the computational methods and their implementation for complex systems reliability and sequential failure logic. To overcome the limitations in sequential failure analysis and the failure analysis of complex systems with multiple failures three new methods and hardware-based implementation are developed.; Existing methods for assessing the reliability and safety of a system with sequential failures assume that the sequences of the failures are given, which is not the case in real life situations. Therefore, the sequences of the failures should be identified and the probability of their occurrence should be determined. The identification and analysis of sequential failures method identifies the possible sequences of failures and computes the probability of their occurrence.; Current Petri net-based failure analysis methods first, imply that the times between failures of different components are the same and constant; and, second, do not take into the consideration the complex Petri net structures, for example, inhibitor arcs. The failure analysis based on the markings of Petri net method is developed to deal with complex Petri net structures and different failure rates of basic events.; It is discovered that the marking-based method is not flexible for sequential failure analysis and cannot be applied directly to the Timed Petri net. Therefore, the method of failure analysis based on the concept of counters of Petri net simulation is developed. The counters-based method is designed to deal with complex Petri net structures and compute sequential failure probabilities.; The hardware-based implementation of counters-based method is developed. Different structures of Petri net are mapped into the circuits. The prototype of a simple manufacturing assembly system is developed. The testing of the prototype demonstrated the feasibility and accuracy of the method.
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