<p>This study introduces a novel methodology for assessing sequential failures in Petri Nets by focusing on transition firings rather than token counts. By utilizing counters to track transition firings, the approach shifts from traditional methods that rely on markings for reliability analysis, such as the Markovian approach and Visual SLAM AWESIM. This method enables a more accurate assessment of sequential failure probabilities and provides a clearer understanding of system dynamics. The proposed approach is advantageous in handling large systems as it avoids state-space explosion and supports diverse failure time distributions. It requires fewer variables and computational resources compared to existing methods like those by Yang and Liu, while also simplifying the retrieval of markings from counters. This makes it an effective tool for risk and failure assessment, offering valuable insights for enhancing system reliability and safety. In industrial and autonomous robotics, where reliability and safety are critical, this methodology allows robots to manage internal failures without immediate human intervention. The study employs failure mode effect analysis (FMEA) and fault tree analysis (FTA) to detect and analyze component failures. Integrating Petri Nets into the analysis helps determine the average rate of system failures by monitoring the markings of Petri Net models. This approach facilitates efficient modeling of system failures and reliability analysis, streamlining computation and improving process safety. Overall, the methodology offers a comprehensive solution for evaluating system reliability and safety, contributing to better design and operation in complex systems.</p>