{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:16:17Z","timestamp":1763468177120,"version":"3.41.0"},"reference-count":34,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2014,3,1]],"date-time":"2014-03-01T00:00:00Z","timestamp":1393632000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Storage"],"published-print":{"date-parts":[[2014,3]]},"abstract":"<jats:p>We introduce a new closed-form equation for estimating the number of data-loss events for a redundant array of inexpensive disks in a RAID-6 configuration. The equation expresses operational failures, their restorations, latent (sector) defects, and disk media scrubbing by time-based distributions that can represent non-homogeneous Poisson processes. It uses two-parameter Weibull distributions that allows the distributions to take on many different shapes, modeling increasing, decreasing, or constant occurrence rates. This article focuses on the statistical basis of the equation. It also presents time-based distributions of the four processes based on an extensive analysis of field data collected over several years from 10,000s of commercially available systems with 100,000s of disk drives. Our results for RAID-6 groups of size 16 indicate that the closed-form expression yields much more accurate results compared to the MTTDL reliability equation and matching computationally-intensive Monte Carlo simulations.<\/jats:p>","DOI":"10.1145\/2577386","type":"journal-article","created":{"date-parts":[[2014,4,1]],"date-time":"2014-04-01T13:06:54Z","timestamp":1396357614000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":28,"title":["Beyond MTTDL"],"prefix":"10.1145","volume":"10","author":[{"given":"Jon G.","family":"Elerath","sequence":"first","affiliation":[{"name":"Reliability Consulting Services"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiri","family":"Schindler","sequence":"additional","affiliation":[{"name":"NetApp"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2014,3]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"4","article-title":"Statistical methods in reliability","volume":"25","author":"Ascher H.","year":"1983","journal-title":"Discussion. Technometrics"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/24.784271"},{"key":"e_1_2_1_3_1","unstructured":"Ascher H. 2010. Personal communication.  Ascher H. 2010. Personal communication."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1269899.1254917"},{"volume-title":"Proceedings of the 6th USENIX Conference on File and Storage Technologies.","author":"Bairavasundaram L.","key":"e_1_2_1_5_1"},{"key":"e_1_2_1_6_1","unstructured":"Bartlett J. Bartlett W. Carr R. Garcia D. Gray J. Horst R. Jardine R. Lenoski D. and McGuire D. 1990. Fault tolerance in tandem computers. NetApp Tech. rep. 90.5.  Bartlett J. Bartlett W. Carr R. Garcia D. Gray J. Horst R. Jardine R. Lenoski D. and McGuire D. 1990. Fault tolerance in tandem computers. NetApp Tech. rep. 90.5."},{"key":"e_1_2_1_7_1","unstructured":"Bazovsky I. 1961. Reliability Theory and Practice. Prentice Hall.  Bazovsky I. 1961. Reliability Theory and Practice . Prentice Hall."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/191995.192033"},{"volume-title":"Proceedings of the 3rd USENIX Conference on File and Storage Technologies.","author":"Corbett P.","key":"e_1_2_1_9_1"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1140103.1140326"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/DSN.2009.5270303"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1317394.1317403"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2008.163"},{"key":"e_1_2_1_14_1","unstructured":"EMC. 2007. EMC CLARiion RAID 6 Technology: A detailed review. http:\/\/www.emc.com\/collateral\/hardware\/white-papers\/h2891-clariion-raid-6.pdf. (Last accessed July 2012.)  EMC. 2007. EMC CLARiion RAID 6 Technology: A detailed review. http:\/\/www.emc.com\/collateral\/hardware\/white-papers\/h2891-clariion-raid-6.pdf. (Last accessed July 2012.)"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/NAS.2010.11"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1993.1002"},{"volume-title":"Proceedings of the 2nd USENIX Conference on Hot Topics in Storage and File Systems.","author":"Greenan K.","key":"e_1_2_1_17_1"},{"key":"e_1_2_1_18_1","unstructured":"Kececioglu D. 1993. Reliability & Life Testing Handbook Volumes 1 & 2. Prentice Hall.  Kececioglu D. 1993. Reliability & Life Testing Handbook Volumes 1 & 2 . Prentice Hall."},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1993.1013"},{"key":"e_1_2_1_20_1","doi-asserted-by":"crossref","unstructured":"Nelson W. 1982. Applied Life Data Analysis. Addison-Wesley.  Nelson W. 1982. Applied Life Data Analysis . Addison-Wesley.","DOI":"10.1002\/0471725234"},{"key":"e_1_2_1_21_1","doi-asserted-by":"crossref","unstructured":"Nelson W. 1990. Accelerated Testing. Wiley & Sons.  Nelson W. 1990. Accelerated Testing . Wiley & Sons.","DOI":"10.1002\/9780470316795"},{"key":"e_1_2_1_22_1","doi-asserted-by":"crossref","unstructured":"Nelson W. 2003. Recurrent Events Data Analysis for Product Repairs Disease Recurrences and Other Applications. ASA-SIAM Series on Statistics and Applied Probability Society for Industrial and Applied Mathematics.   Nelson W. 2003. Recurrent Events Data Analysis for Product Repairs Disease Recurrences and Other Applications . ASA-SIAM Series on Statistics and Applied Probability Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9780898718454"},{"key":"e_1_2_1_23_1","unstructured":"NetApp. 2013. NetApp data ONTAP 8 operating system.http:\/\/www.netapp.com\/us\/products\/platform-os\/data-ontap-8\/index.aspx.  NetApp. 2013. NetApp data ONTAP 8 operating system.http:\/\/www.netapp.com\/us\/products\/platform-os\/data-ontap-8\/index.aspx."},{"key":"e_1_2_1_24_1","unstructured":"Oracle. 2010. A better RAID strategy for high capacity drives in mainframe storage. http:\/\/www.oracle.com\/technetwork\/articles\/systems-hardware-architecture\/raid-strategy-hi-capacity -drives-170907.pdf.  Oracle. 2010. A better RAID strategy for high capacity drives in mainframe storage. http:\/\/www.oracle.com\/technetwork\/articles\/systems-hardware-architecture\/raid-strategy-hi-capacity -drives-170907.pdf."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/PRDC.2009.66"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/50202.50214"},{"volume-title":"Proceedings of the 5th USENIX Conference on File and Storage Technologies.","author":"Pinheiro E.","key":"e_1_2_1_27_1"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/DSN.2006.61"},{"volume-title":"Proceedings of the 5th USENIX Conference on File and Storage Technologies.","author":"Schroeder B.","key":"e_1_2_1_29_1"},{"key":"e_1_2_1_30_1","unstructured":"Serve The Home. 2011. The RAID reliability anthology -- The primer. http:\/\/www.servethehome.com\/raid-reliability-failureanthology-part-primer.  Serve The Home. 2011. The RAID reliability anthology -- The primer. http:\/\/www.servethehome.com\/raid-reliability-failureanthology-part-primer."},{"volume-title":"Proceedings of the IEEE Reliability and Maintainability Symposium.","author":"Shah S.","key":"e_1_2_1_31_1"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1981.10486230"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/1629075.1629076"},{"key":"e_1_2_1_34_1","doi-asserted-by":"crossref","unstructured":"Tobias P. and Trindade D. 2011. Applied Reliability3rd Ed. CRC Press.  Tobias P. and Trindade D. 2011. Applied Reliability 3rd Ed. CRC Press.","DOI":"10.1201\/b11787"}],"container-title":["ACM Transactions on Storage"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2577386","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2577386","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:55:54Z","timestamp":1750229754000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2577386"}},"subtitle":["A Closed-Form RAID 6 Reliability Equation"],"short-title":[],"issued":{"date-parts":[[2014,3]]},"references-count":34,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,3]]}},"alternative-id":["10.1145\/2577386"],"URL":"https:\/\/doi.org\/10.1145\/2577386","relation":{},"ISSN":["1553-3077","1553-3093"],"issn-type":[{"type":"print","value":"1553-3077"},{"type":"electronic","value":"1553-3093"}],"subject":[],"published":{"date-parts":[[2014,3]]},"assertion":[{"value":"2013-03-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2013-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-03-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}