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In this paper, we argue that the reliability of large-scale storage systems can be significantly improved by using better reliability metrics and more efficient policies for recovering from hardware failures. Specifically, we make three main contributions. First, we introduce NDS (Normalcy Deviation Score), a new metric for dynamically quantifying the reliability status of a storage system. Second, we propose MinI (Minimum Intersection), a novel recovery scheduling policy that improves reliability by efficiently reconstructing data after a hardware failure. MinI uses NDS to tradeoff reliability and performance in making its scheduling decisions. Third, we evaluate NDS and MinI for three common data-allocation schemes and a number of different parameters. Our evaluation focuses on a distributed storage system based on erasure codes. We find that MinI improves reliability significantly, as compared to conventional policies.