Fault-Tolerant Design

194 Pages·2013·2.309 MB·English

by  Elena Dubrova (auth.)

Elena Dubrova
Fault-Tolerant
Design
Fault-Tolerant Design
Elena Dubrova
Fault-Tolerant Design
123
Elena Dubrova
KTHRoyal InstituteofTechnology
Krista
Sweden
ISBN 978-1-4614-2112-2 ISBN 978-1-4614-2113-9 (eBook)
DOI 10.1007/978-1-4614-2113-9
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2013932644
(cid:2)SpringerScience+BusinessMediaNewYork2013
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To my mother
Preface
This textbook serves as an introduction to fault tolerance, intended for upper
division undergraduate students, graduate-level students, and practicing engineers
in need of an overview of the field. Readers will develop skills in modeling and
evaluating fault-tolerant architectures in terms of reliability, availability, and
safety. They will gain a thorough understanding of fault-tolerant computing,
including both the theory of how to achieve fault tolerance through hardware,
software, information, and time redundancy and the practical knowledge of
designing fault-tolerant hardware and software systems.
Thebookcontainseightchapterscoveringthefollowingtopics.Chapter1isan
introduction, discussing the importance of fault tolerance in developing a
dependable system. Chapter 2 describes three fundamental characteristics of
dependability: attributes, impairment, and means. Chapter 3 introduces depend-
ability evaluation techniques and dependability models such as reliability block
diagrams and Markov chains. Chapter 4 presents commonly used approaches for
the design offault-tolerant hardware systems, such as triple modular redundancy,
standby redundancy, and self-purging redundancy and evaluates their effect on
system dependability. Chapter 5 shows how fault tolerance can be achieved by
means of coding. It covers many important families of codes, including parity,
linear, cyclic, unordered, and arithmetic codes. Chapter 6 presents time redun-
dancy techniques which can be used for detecting and correcting transient and
permanentfaults.Chapter7describesthemainapproachesforthedesignoffault-
tolerant software systems, including checkpoint and restart, recovery blocks,
N-version programming, and N self-checking programming. Chapter 8 concludes
the book.
The content is designed to be highly accessible, including numerous examples
andproblemstoreinforce the materiallearned.Solutions toproblems andPower-
Point slides are available from the author upon request.
Stockholm, Sweden, December 2012 Elena Dubrova
vii
Acknowledgments
Thisbookhasevolvedfromthelecturenotesofthecourse‘‘DesignofFault-Tolerant
Systems’’thatIhavetaughtattheRoyalInstituteofTechnology(KTH),since2000.
Throughouttheyears,manystudentsandcolleagueshavehelpedmepolishthetext.
Iamgratefultoallwhogavemefeedback.Inparticular,IwouldliketothankNanLi,
ShohrehSharifMansouri,NasimFarahini,BayronNavas,JonianGrazhdani,Xavier
Lowagie,PieterNuyts,HenrikKirkeby,ChenFu,KareemRefaat,SergejKoziner,
JuliaKuznetsova,ZhonghaiLu,andRomanMorawekforfindingmultiplemistakes
and suggesting valuable improvements in the manuscript. I am grateful to Hannu
Tenhunenwhoinspiredmetoteachthiscourseandconstantlysupportedmeduring
my academic career. I am also indebted to Charles Glaser from Springer for his
encouragementandassistanceinpublishingthebookandtoSandraBrunsbergfor
herverycarefulproofreadingofthefinaldraft.Specialthankstoafriendofminewho
advised metousetheMetaPost toolfordrawingpictures.Indeed,MetaPost gives
perfectresults.
Finally, I am grateful to the Swedish Foundation for International Cooperation
in Research and Higher Education (STINT), for the scholarship KU2002-4044
whichsupportedmytriptotheUniversityofNewSouthWales,Sydney,Australia,
where the first draft of this book was written during October–December 2002.
ix
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Definition of Fault Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Fault Tolerance and Redundancy. . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Applications of Fault Tolerance . . . . . . . . . . . . . . . . . . . . . . . 2
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Fundamentals of Dependability . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Dependability Attributes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Dependability Impairments. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 Faults, Errors, and Failures. . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 Origins of Faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.3 Common-Mode Faults. . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.4 Hardware Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.5 Software Faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Dependability Means. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 Fault Tolerance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.2 Fault Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.3 Fault Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.4 Fault Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Dependability Evaluation Techniques. . . . . . . . . . . . . . . . . . . . . . 21
3.1 Basics of Probability Theory. . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Common Measures of Dependability. . . . . . . . . . . . . . . . . . . . 24
3.2.1 Failure Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.2 Mean Time to Failure . . . . . . . . . . . . . . . . . . . . . . . . . 27
xi
xii Contents
3.2.3 Mean Time to Repair . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.4 Mean Time Between Failures. . . . . . . . . . . . . . . . . . . . 30
3.2.5 Fault Coverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Dependability Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 Reliability Block Diagrams . . . . . . . . . . . . . . . . . . . . . 31
3.3.2 Fault Trees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.3 Reliability Graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.4 Markov Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Dependability Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4.1 Reliability Evaluation Using Reliability
Block Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4.2 Dependability Evaluation Using Markov Processes. . . . . 39
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4 Hardware Redundancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1 Redundancy Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Passive Redundancy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.1 Triple Modular Redundancy. . . . . . . . . . . . . . . . . . . . . 58
4.2.2 N-Modular Redundancy. . . . . . . . . . . . . . . . . . . . . . . . 63
4.3 Active Redundancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3.1 Duplication with Comparison. . . . . . . . . . . . . . . . . . . . 65
4.3.2 Standby Redundancy. . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.3 Pair-And-A-Spare . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Hybrid Redundancy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4.1 Self-Purging Redundancy. . . . . . . . . . . . . . . . . . . . . . . 76
4.4.2 N-Modular Redundancy with Spares. . . . . . . . . . . . . . . 79
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Information Redundancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1 History. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Fundamental Notions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.1 Code. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.2 Encoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.3 Information Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.4 Decoding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.5 Hamming Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.6 Code Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 Parity Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.1 Definition and Properties. . . . . . . . . . . . . . . . . . . . . . . 92
5.3.2 Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.3 Horizontal and Vertical Parity Codes. . . . . . . . . . . . . . . 95
Contents xiii
5.4 Linear Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4.1 Basic Notions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4.2 Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.4.3 Generator Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.4.4 Parity Check Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.4.5 Syndrome. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.4.6 Construction of Linear Codes. . . . . . . . . . . . . . . . . . . . 102
5.4.7 Hamming Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4.8 Lexicographic Parity Check Matrix. . . . . . . . . . . . . . . . 107
5.4.9 Applications of Hamming Codes . . . . . . . . . . . . . . . . . 108
5.4.10 Extended Hamming Codes. . . . . . . . . . . . . . . . . . . . . . 109
5.5 Cyclic Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5.1 Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5.2 Polynomial Manipulation. . . . . . . . . . . . . . . . . . . . . . . 111
5.5.3 Generator Polynomial . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5.4 Parity Check Polynomial . . . . . . . . . . . . . . . . . . . . . . . 114
5.5.5 Syndrome Polynomial . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.5.6 Implementation of Encoding and Decoding . . . . . . . . . . 115
5.5.7 Separable Cyclic Codes. . . . . . . . . . . . . . . . . . . . . . . . 118
5.5.8 Cyclic Redundancy Check Codes . . . . . . . . . . . . . . . . . 121
5.5.9 Reed-Solomon Codes . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.6 Unordered Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.6.1 M-of-N Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.6.2 Berger Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.7 Arithmetic Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.7.1 AN Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.7.2 Residue Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6 Time Redundancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.1 Transient Faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.2 Permanent Faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.2.1 Alternating Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.2.2 Recomputing with Modified Operands. . . . . . . . . . . . . . 142
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7 Software Redundancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.1 Software Versus Hardware. . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.2 Single-Version Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.2.1 Fault Detection Techniques . . . . . . . . . . . . . . . . . . . . . 159
7.2.2 Fault Containment Techniques . . . . . . . . . . . . . . . . . . . 160
7.2.3 Fault Recovery Techniques . . . . . . . . . . . . . . . . . . . . . 161