Reliability Analysis of Aerospace system using Sumudu Transform with Fermatean Fuzzy Sets

This research presents a comprehensive reliability analysis of a fault-tolerant Flight Control System (FCS) modeled as a hierarchical (3-out-of-4)-within-(2-out-of-3):G system, reflecting the complex redundancy structures essential for aerospace safety-critical applications. By integrating copula-based dependency modeling among subsystem components with the Universal Generating Function (UGF) approach at the system level, the research effectively captures both component correlations and overall system reliability. The application of the Sumudu transform facilitated the analytical solution of the continuous-time Markov process describing subsystem state transitions, enabling the precise evaluation of reliability and availability under both repairable and non-repairable scenarios. The numerical results demonstrate that the hierarchical redundancy architecture maintains exceptionally high reliability and availability over the mission time with minimal degradation, underscoring the robustness of the design. Incorporating Fermatean fuzzy sets to model uncertainty in failure rates further enhances the analysis by providing flexible and realistic representations of imprecise reliability parameters. Fuzzy reliability and fuzzy Mean Time to Failure (MTTF) assessments revealed well-defined uncertainty bounds, enabling more informed risk-aware decision-making. Fuzzy cost analysis, leveraging membership and non-membership degrees, identified optimal preventive replacement times that maximize expected profit, highlighting the economic implications of reliability under uncertainty. Overall, the Copula-UGF-based hierarchical modeling framework, combined with advanced fuzzy uncertainty quantification, offers a powerful and adaptable toolset for designing, analyzing, and economically optimizing fault-tolerant aerospace systems. Mathematics Subject Classification: 90B25, 62N05, 60K10, 60K20