Wang, RuidaLyu, HaoOzkut, Murat2026-01-252026-01-2520250748-80171099-1638https://doi.org/10.1002/qre.70143https://hdl.handle.net/20.500.14365/8617In this paper, a polygonal k-out-of-n:F system reliability model is established, where subsystems may share components within the polygon. Components are exposed to a combination of extreme shocks and delta-shock. The reliability of each subsystem's components is modeled using a phase-type distribution and Markov chain approach, with component reliability being incorporated into subsystem reliability calculations. Disjoint cases are classified based on the number of failed components in shared regions to derive the shared component failure probability matrix and the initial probability distribution. Using the transfer matrix and transition rate matrix, the overall system reliability is determined through the Markov chain embedding approach. For this model, the total cost function of the system was determined by calculating the cost functions of different scenarios and different subsystems, and the optimal maintenance time for the system was obtained. The effectiveness of the method is verified by taking the unmanned aerial vehicle swarm working in a harsh environment as an example.eninfo:eu-repo/semantics/closedAccessK-Out-Of-N:F SystemMaintenance PolicyMarkov ChainPhase-Type DistributionShock ModelArticle10.1002/qre.701432-s2.0-105026049687