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In current Cloud computing environments, management of data reliability has become a challenge. For data-intensive scientific applications, storing data in the Cloud with the typical 3-replica replication strategy for managing the data reliability would incur huge storage cost. To address this issue, in this paper we present a novel cost-effective data reliability management mechanism named PRCR, which proactively checks the availability of replicas for maintaining data reliability. Our simulation indicates that, comparing with the typical 3-replica replication strategy, PRCR can reduce the storage space consumption by one-third to two-thirds, hence reduce the storage cost significantly in the Cloud.