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This paper presents a new model for analyzing the repairability of reconfigurable system-on-chip (RSoC) instrumentation with the repair process. It exploits the connectivity of the interconnected cores in which unreliability factors due to both neighboring cores and the interconnect structure are taken into account. Based on the connectivity, two RSoC repair scheduling strategies, Minimum Number of Interconnections First (I-MIN) and Minimum Number of Neighboring Cores First (C-MIN), are proposed. Two other scheduling strategies, Maximum Number of Interconnections First (I-MAX) and Maximum Number of Neighboring cores First (C-MAX), are also introduced and analyzed to further explore the impact of connectivity-based repair scheduling on the overall repairability of RSoCs. Extensive parametric simulations demonstrate the efficiency of the proposed RSoC repair scheduling strategies; thereby manufacturing ultimately reliable RSoC instrumentation can be achieved.