A Unified Reliability Model for Fault-Tolerant Computers

Wang, Ying; Avizienis,

doi:10.1109/tc.1980.1675495

Cited by 71 publications

(6 citation statements)

References 12 publications

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“…The lower bound in (8) in Theorem 1 can take negative values for certain t ≥ 0. If the lower bound is negative for a given t ≥ 0, the result of Theorem 1 becomes trivial; however, in the following example we present a situation in which (8) produces a meaningful lower bound for the MIT of a gamma-distributed random lifetime.…”

Section: Usual Stochastic Order-based Bounds For the Idle Time Of Col...mentioning

confidence: 99%

“…A situation in which such a standby system is used is that of k-out-of-n systems (see, e.g., Levitin et al [1], Fernández [2], Barron and Yechiali [3], Barron [4], Levitin et al [5], Bian et al [6], and references therein). The method of cold standby has been widely utilized in crucial scenarios such as flight controls, satellites, chemical process controls, telecommunication systems, and nuclear power plants (see, for instance, Mathur [7], Wang [8], Johnson and Julich [9], Sinaki [10], Pandey et al [11], Coit [12], Hsieh and Hsieh [13], Elerath and Pecht [14], and Wang et al [15]).…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Orderings of the Idle Time of Inactive Standby Systems

Shrahili,

Kayid

2023

Mathematics

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In this paper, we consider a failed cold standby system and obtain stochastic bounds on the idle time of such systems. We state and prove that if the last spare in the system is exponentially distributed and if the components have log-concave lifetime distributions, then the idle time of a failed cold standby system is smaller than the sum of the idle times of the components in the system according to the likelihood ratio order. In order to compare the idle time of two cold standby systems with different numbers of spares and different observation times of the failure in terms of the likelihood ratio order, an additional result is presented. Finally, we establish sufficient conditions for the usual stochastic ordering between the idle time of a cold standby system of size two and the sum of the idle times of the components in the system. We provide several examples to show that the results are achievable.

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Section: Usual Stochastic Order-based Bounds For the Idle Time Of Col...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic Orderings of the Idle Time of Inactive Standby Systems

Shrahili,

Kayid

2023

Mathematics

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“…From a TCO viewpoint SSDs will be preferred when they are less than 5-fold expensive than HDDs per GB. 158 Distributed SSD -DSSD Flash coding is based on Grid files in Section 3.1 Bonwick 2014 [23]. An obvious problem with DDSD is that check strips chips will be updated more often than data chips A:31 and susceptible to earlier failures.…”

Section: Flash Solid State Drives -Ssdsmentioning

confidence: 99%

“…An example of this effort was a reliability expression derived for a a hybrid k-out-of-n system with n components energized reported in Mathur and Avizienis [141], which is given in Example 3.32 in Trivedi 2001 [249]. Aries is a unifying method for analyzing closed systems Ng and Avizienis 1980 [158]. The parameters used in this study given in The reliability of a closed fault-tolerant system is expressed as:…”

Section: Automated Reliability Interactive Estimation System -Aries P...mentioning

confidence: 99%

“…In the case of RAID5 a second disk failure or unreadable sector will lead to data loss as discussed in Section 11.5. Section 5.4 titled "Imperfect Fault Coverage and Reliability" in Trivedi 2001 [249] provides a good discussion and formulas derived in Ng and Avizienis [158]. Section 8.5 titled "Markov Chains with Absorbing States" A:89…”

Section: Disk Scrubbing and Intradisk Redundancy To Deal With Lsesmentioning

confidence: 99%

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Reliability and Performance of Mirrored Disk Organizations

Thomasian

2008

The Computer Journal

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This is a followup to the 1994 tutorial by Berkeley RAID researchers whose 1988 RAID paper foresaw a revolutionary change in storage industry based on advances in magnetic disk technology, i.e., replacement of large capacity expensive disks with arrays of small capacity inexpensive disks. NAND flash SSDs which use less power, incur very low latency, provide high bandwidth, and are more reliable than HDDs are expected to replace HDDs as their prices drop. Replication in the form of mirrored disks and erasure coding via parity and Reed-Solomon codes are two methods to achieve higher reliability through redundancy in disk arrays. RAID(4+k), k=1,2,... arrays utilizing k check strips makes them k-disk-failure-tolerant with maximum distance separable coding with minimum redundancy. Clustered RAID, local recovery codes, partial MDS, and multilevel RAID are proposals to improve RAID reliability and performance. We discuss RAID5 performance and reliability analysis in conjunction with HDDs w/o and with latent sector errors -LSEs, which can be dealt with by intradisk redundancy and disk scrubbing, the latter enhanced with machine learning algorithms. Undetected disk errors causing silent data corruption are propagated by rebuild. We utilize the M/G/1 queueing model for RAID5 performance evaluation, present approximations for fork/join response time in degraded mode analysis, and the vacationing server model for rebuild analysis. Methods and tools for reliability evaluation with Markov chain modeling and simulation are discussed. Queueing and reliability analysis are based on probability theory and stochastic processes so that the two topics can be studied together. Their application is presented here in the context of RAID arrays in a tutorial manner.

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Imperfect Preventive Maintenance

Springer Series in Reliability Engineering

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A Unified Reliability Model for Fault-Tolerant Computers

Cited by 71 publications

References 12 publications

Stochastic Orderings of the Idle Time of Inactive Standby Systems

Stochastic Orderings of the Idle Time of Inactive Standby Systems

Reliability and Performance of Mirrored Disk Organizations

Imperfect Preventive Maintenance

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