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In this paper we address issues of reliability of RAID systems. We focus on"big data" systems with a large number of drives and advanced error correctionschemes beyond \RAID{6}. Our RAID paradigm is based on Reed-Solomon codes, andthus we assume that the RAID consists of $N$ data drives and $M$ check drives.The RAID fails only if the combined number of failed drives and sector errorsexceeds $M$, a property of Reed-Solomon codes.  We review a number of models considered in the literature and build upon themto construct models usable for a large number of data and check drives. Weattempt to account for a significant number of factors that affect RAIDreliability, such as drive replacement or lack thereof, mistakes during servicesuch as replacing the wrong drive, delayed repair, and the finite duration ofRAID reconstruction. We evaluate the impact of sector failures that do notresult in drive replacement.  The reader who needs to consider large $M$ and $N$ will find applicablemathematical techniques concisely summarized here, and should be able to applythem to similar problems. Most methods are based on the theory of continuoustime Markov chains, but we move beyond this framework when we consider thefixed time to rebuild broken hard drives, which we model using systems of delayand partial differential equations.  One universal statement is applicable across various models: increasing thenumber of check drives in all cases increases the reliability of the system,and is vastly superior to other approaches of ensuring reliability such asmirroring.

On the Reliability of RAID Systems: An Argument for More Check Drives