A Five-State Markov Reliability Model for GEO Satellites with Sequential Degradation, Sudden Critical Transitions, and Functional Restoration

Long-term GEO satellite operation requires reliability models that distinguish full mission capability from degraded but still functional states and from critical functional loss. This study develops a five-state Markov reliability model in which states S0–S4 represent successive levels of mission capability. The model integrates sequential degradation, a direct S0 → S4 transition representing sudden critical events, and functional restoration associated with redundancy, FDIR, reconfiguration, and software-supported recovery. Four computational variants were analysed over a segmented 15-year mission horizon to separate the influence of these mechanisms. The transition intensities were specified for a reference scenario rather than estimated for a specific GEO mission. Full and retained mission capability were evaluated using Rfull = P0 and Rpartial = 1 − P4. For the complete model, these measures reached 0.6926 and 0.9633 after 15 years, respectively. Calculations performed in MATLAB 2025 using the matrix exponential method were independently verified by numerical integration, with agreement within approximately 10−14. The framework provides a reproducible basis for analysing long-term GEO satellite functional reliability under different degradation and restoration scenarios.