Petri net is a powerful technique widely used in modeling and analysis of complex systems and processes such as manufacturing systems and nuclear power plants. Due to its capability in modeling the dynamics of the systems, Petri net has been combined with fault tree analysis techniques to determine the failure rates of the systems. Although a promising approach, current methods in combining Petri net with fault tree analysis for determining system failure rates assume that the failure rates of the basic events in a system are the same and the Petri net model of the system consists of simple structures. These assumptions do not reflect the real industrial applications for system failure analysis in an agile manufacturing environment. To overcome the limitations of the current methods in applying Petri net for failure and safety assessment of systems, this paper extends the current methods to real applications where basic events can have different failure rates and the systems can be modeled with complex Petri net structures. An example of failure analysis of a robotic manufacturing cell is provided to demonstrate the developed methods.