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doi:10.1016/j.jss.2006.02.035 
Copyright © 2006 Elsevier Inc. All rights reserved.
Shortcut method for reliability comparisons in RAID
Alexander Thomasian
, a, 
Received 19 August 2005;
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Abstract
Given that the reliability of each disk in a disk array during its useful lifetime is given as r = 1 − 
with 
1, we show that the reliability of a RAID disk array tolerating all possible n − 1 disk failures can be specified as R ≈ 1 − ann, where an is the smallest nonzero coefficient in the corresponding asymptotic expansion, e.g., for n-way replication R = 1 − n. We compare the reliability of several mirrored disk organizations, which provide tradeoffs between reliability and load balancedness (after disk failure) by comparing their a2 values, which can be obtained via a partial reliability analysis taking into account a few disk failures. We next use asymptotic expansions to compare the reliability of hierarchical RAID disk arrays, which combine replication and rotated parity disk arrays (RAID5 and RAID6). Finally, we argue that the mean time to data loss in systems with repair is related to the reliability without repair. As part of this discussion we show how to estimate the mean time to data loss in RAID5 and RAID6 disk arrays without resorting to transient analysis.
Keywords: Redundant Arrays of Independent Disks – RAID; Mirrored disks; Multilevel RAID arrays; Reliability modeling; Asymptotic expansions; Hierarchical RAID; RAID repair; Rebuild time
Abbreviations: BM, basic mirroring; CD, chained declustering; GRD, group rotated declustering; ID, interleaved declustering; JBOD, just a bunch of disks; kDFT, k disk failure tolerant; LSF, latent sector failure; MTTDL, mean time to data loss; MTTF, mean time to failure; MTTR, mean time to repair; RAIDi, RAID level i; RDP, rotated diagonal parity
Article Outline
- 1. Introduction
- 2. Asymptotic reliability expression
- 3. RAID1 organizations and their reliability
- 3.1. Basic mirroring with N disks
- 3.2. Group rotate declustering
- 3.3. Interleaved declustering
- 3.4. Chained declustering
- 3.5. RAID1 reliability comparison
- 4. RAID5, RAID6, and multilevel RAID
- 5. Reliability modeling
- 6. Conclusions
- Acknowledgements
- Appendix. Repair time in RAID5
- References
