EN 61078:2016
(Main)Reliability block diagrams
Reliability block diagrams
IEC 61078:2016 this International Standard describes: - the requirements to apply when reliability block diagrams (RBDs) are used in dependability analysis; - the procedures for modelling the dependability of a system with reliability block diagrams; - how to use RBDs for qualitative and quantitative analysis; - the procedures for using the RBD model to calculate availability, failure frequency and reliability measures for different types of systems with constant (or time dependent) probabilities of blocks success/failure, and for non-repaired blocks or repaired blocks; - some theoretical aspects and limitations in performing calculations for availability, failure frequency and reliability measures; - the relationships with fault tree analysis (see IEC 61025) and Markov techniques (see IEC 61165). This third edition cancels and replaces the second edition published in 2006. This edition constitutes a technical revision. This edition includes the following significant technical changes with respect to the previous edition: - the structure of the document has been entirely reconsidered, the title modified and the content extended and improved to provide more information about availability, reliability and failure frequency calculations; - Clause 3 has been extended and clauses have been introduced to describe the electrical analogy, the "non-coherent" RBDs and the "dynamic" RBDs; - Annex B about Boolean algebra methods has been extended; - Annex C (Calculations of time dependent probabilities), Annex D (Importance factors), Annex E (RBD driven Petri net models) and Annex F (Numerical examples and curves) have been introduced. Keywords: reliability block diagram (RBD)
Zuverlässigkeitsblockdiagramme
Diagrammes de fiabilité
L'IEC 61078:2016 la présente Norme internationale décrit: - les exigences à appliquer lors de l'utilisation de diagrammes de fiabilité (BDF) dans le cadre d'analyses de sûreté de fonctionnement; - les procédures de modélisation de la sûreté de fonctionnement d'un système avec des diagrammes de fiabilité; - comment utiliser les BDF pour procéder à des analyses qualitatives et quantitatives; - les procédures d'utilisation du modèle BDF pour calculer les mesures de disponibilité, de fréquence de défaillance et de fiabilité pour différents types de systèmes avec des probabilités constantes (ou dépendant du temps) de succès/défaillance de blocs, et ceci pour des blocs non réparés ou des blocs réparés; - certains aspects et limitations théoriques liés aux calculs des mesures de disponibilité, de fréquence de défaillance et de fiabilité; - les relations avec l'analyse par arbre de panne (voir IEC 61025) et les techniques de Markov (voir IEC 61165). Cette troisième édition annule et remplace la deuxième édition publiée en 2006. Cette édition constitue une révision technique. Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente: - la structure du document a été entièrement remaniée, le titre modifié et le contenu étendu et amélioré afin de fournir de plus amples informations sur les calculs de disponibilité, de fiabilité et de fréquence de défaillance; - l'Article 3 a été étendu et des articles ont été introduits pour décrire l'analogie électrique, les BDF "non cohérents" et les BDF "dynamiques"; - l'Annexe B relative aux méthodes algébriques booléennes a été étendue; - l'Annexe C (Calculs des probabilités en fonction du temps), l'Annexe D (Facteurs d'importance), l'Annexe E (Modèles de réseau de Petri piloté par BDF) et l'Annexe F (Exemples numériques et courbes) ont été introduites. Mots clés: diagrammes de fiabilité (BDF)
Zanesljivost, blokovni diagrami (IEC 61078:2016)
Ta mednarodni standard opisuje:
• zahteve, ki jih je treba izpolniti, ko se za analizo zagotovljivosti uporabljajo blokovni diagrami zanesljivosti (RBD);
• postopke za modeliranje zagotovljivosti sistema z blokovnimi diagrami zanesljivosti;
• uporabo blokovnih diagramov zanesljivosti za kvalitativne in kvantitativne analize;
• postopke za uporabo modela blokovnih diagramov zanesljivosti za izračun ukrepov razpoložljivosti, pogostosti odpovedi in zanesljivosti za različne vrste sistemov s konstantno (ali časovno odvisno)
verjetnostjo blokov uspeha/neuspeha ter za nepopravljene ali popravljene bloke;
• nekatere teoretske vidike in omejitve pri izvajanju izračunov za ukrepe razpoložljivosti, pogostosti odpovedi in zanesljivosti;
• odnose z analizo drevesa okvar (glejte standard IEC 61025 [1]) in Markove tehnike (glejte standard IEC 61165 [2]).
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-januar-2017
1DGRPHãþD
SIST EN 61078:2007
Zanesljivost, blokovni diagrami (IEC 61078:2016)
Reliability block diagrams (IEC 61078:2016)
Ta slovenski standard je istoveten z: EN 61078:2016
ICS:
03.120.01 Kakovost na splošno Quality in general
21.020 =QDþLOQRVWLLQQDþUWRYDQMH Characteristics and design of
VWURMHYDSDUDWRYRSUHPH machines, apparatus,
equipment
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EUROPEAN STANDARD EN 61078
NORME EUROPÉENNE
EUROPÄISCHE NORM
November 2016
ICS 03.120.01; 03.120.99 Supersedes EN 61078:2006
English Version
Reliability block diagrams
(IEC 61078:2016)
Diagrammes de fiabilité Zuverlässigkeitsblockdiagramme
(IEC 61078:2016) (IEC 61078:2016)
This European Standard was approved by CENELEC on 2016-09-16. CENELEC members are bound to comply with the CEN/CENELEC
Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.
Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC
Management Centre or to any CENELEC member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CENELEC member into its own language and notified to the CEN-CENELEC Management Centre has the
same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, the Czech Republic,
Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2016 CENELEC All rights of exploitation in any form and by any means reserved worldwide for CENELEC Members.
Ref. No. EN 61078:2016 E
European foreword
The text of document 56/1685/FDIS, future edition 3 of IEC 61078, prepared by
IEC/TC 56 "Dependability" was submitted to the IEC-CENELEC parallel vote and approved by
CENELEC as EN 61078:2016.
The following dates are fixed:
(dop) 2017-06-16
• latest date by which the document has to be
implemented at national level by
publication of an identical national
standard or by endorsement
• latest date by which the national (dow) 2019-09-16
standards conflicting with the
document have to be withdrawn
This document supersedes EN 61078:2006.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CENELEC [and/or CEN] shall not be held responsible for identifying any or all such
patent rights.
Endorsement notice
The text of the International Standard IEC 61078:2016 was approved by CENELEC as a European
Standard without any modification.
In the official version, for Bibliography, the following notes have to be added for the standards indicated:
IEC 61025 NOTE Harmonized as EN 61025.
IEC 61165 NOTE Harmonized as EN 61165.
IEC 62551 NOTE Harmonized as EN 62551.
IEC 60812 NOTE Harmonized as EN 60812.
IEC 61508:2010 Series NOTE Harmonized as EN 61508:2010 Series.
IEC 61511:2016 Series NOTE Harmonized as EN 61511:2016 Series.
ISO/TR 12489 NOTE Harmonized as CEN ISO/TR 12489.
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
NOTE 1 When an International Publication has been modified by common modifications, indicated by (mod), the relevant
EN/HD applies.
NOTE 2 Up-to-date information on the latest versions of the European Standards listed in this annex is available here:
www.cenelec.eu
Publication Year Title EN/HD Year
IEC 60050-192 - International Electrotechnical Vocabulary - - -
Part 192: Dependability
IEC 61703 - Mathematical expressions for reliability, EN 61703 -
availability, maintainability and
maintenance support terms
IEC 61078 ®
Edition 3.0 2016-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Reliability block diagrams
Diagrammes de fiabilité
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 03.120.01; 03.120.99 ISBN 978-2-8322-3561-4
– 2 – IEC 61078:2016 © IEC 2016
CONTENTS
FOREWORD . 8
INTRODUCTION . 10
1 Scope . 11
2 Normative references. 11
3 Terms and definitions . 11
4 Symbols and abbreviated terms . 18
5 Preliminary considerations, main assumptions, and limitations . 22
5.1 General considerations . 22
5.2 Pre-requisite/main assumptions . 23
5.3 Limitations . 23
6 Establishment of system success/failed states . 24
6.1 General considerations . 24
6.2 Detailed considerations . 24
6.2.1 System operation . 24
6.2.2 Environmental conditions . 25
6.2.3 Duty cycles . 25
7 Elementary models . 25
7.1 Developing the model . 25
7.2 Series structures . 25
7.3 Parallel structures . 26
7.4 Mix of series and parallel structures. 26
7.5 Other structures . 27
7.5.1 m out of n structures . 27
7.5.2 Structures with common blocks . 28
7.5.3 Composite blocks . 29
7.6 Large RBDs and use of transfer gates . 29
8 Qualitative analysis: minimal tie sets and minimal cut sets. . 30
8.1 Electrical analogy . 30
8.2 Series-parallel representation with minimal success path and cut sets . 32
8.3 Qualitative analysis from minimal cut sets . 33
9 Quantitative analysis: blocks with constant probability of failure/success . 33
9.1 Series structures . 33
9.2 Parallel structures . 34
9.3 Mix of series and parallel structures. 34
9.4 m/n architectures (identical items) . 35
10 Quantitative analysis: blocks with time dependent probabilities of failure/success . 35
10.1 General . 35
10.2 Non-repaired blocks . 36
10.2.1 General . 36
10.2.2 Simple non-repaired block . 36
10.2.3 Non-repaired composite blocks. 36
10.2.4 RBDs with non-repaired blocks . 37
10.3 Repaired blocks . 37
10.3.1 Availability calculations . 37
10.3.2 Average availability calculations . 40
IEC 61078:2016 © IEC 2016 – 3 –
10.3.3 Reliability calculations . 42
10.3.4 Frequency calculations . 43
11 Boolean techniques for quantitative analysis of large models . 43
11.1 General . 43
11.2 Method of RBD reduction . 44
11.3 Use of total probability theorem . 45
11.4 Use of Boolean truth tables . 46
11.5 Use of Karnaugh maps . 47
11.6 Use of the Shannon decomposition and binary decision diagrams . 49
11.7 Use of Sylvester-Poincaré formula . 50
11.8 Examples of RBD application. 51
11.8.1 Models with repeated blocks . 51
11.8.2 m out of n models (non-identical items) . 54
12 Extension of reliability block diagram techniques . 54
12.1 Non-coherent reliability block diagrams . 54
12.2 Dynamic reliability block diagrams . 57
12.2.1 General . 57
12.2.2 Local interactions . 58
12.2.3 Systemic dynamic interactions . 59
12.2.4 Graphical representations of dynamic interactions . 59
12.2.5 Probabilistic calculations . 62
Annex A (informative) Summary of formulae . 63
Annex B (informative) Boolean algebra methods . 67
B.1 Introductory remarks . 67
B.2 Notation . 67
B.3 Tie sets (success paths) and cut sets (failure paths) analysis . 68
B.3.1 Notion of cut and tie sets . 68
B.3.2 Series-parallel representation using minimal tie and cut sets . 69
B.3.3 Identification of minimal cuts and tie sets . 70
B.4 Principles of calculations . 71
B.4.1 Series structures . 71
B.4.2 Parallel structures . 71
B.4.3 Mix of series and parallel structures . 73
B.4.4 m out of n architectures (identical items) . 73
B.5 Use of Sylvester Poincaré formula for large RBDs and repeated blocks . 74
B.5.1 General . 74
B.5.2 Sylvester Poincaré formula with tie sets . 74
B.5.3 Sylvester Poincaré formula with cut sets . 76
B.6 Method for disjointing Boolean expressions . 77
B.6.1 General and background . 77
B.6.2 Disjointing principle . 78
B.6.3 Disjointing procedure . 79
B.6.4 Example of application of disjointing procedure . 79
B.6.5 Comments . 81
B.7 Binary decision diagrams . 82
B.7.1 Establishing a BDD . 82
B.7.2 Minimal success paths and cut sets with BDDs . 84
B.7.3 Probabilistic calculations with BDDs . 86
– 4 – IEC 61078:2016 © IEC 2016
B.7.4 Key remarks about the use of BDDs . 87
Annex C (informative) Time dependent probabilities and RBD driven Markov
processes . 88
C.1 General . 88
C.2 Principle for calculation of time dependent availabilities . 88
C.3 Non-repaired blocks . 89
C.3.1 General . 89
C.3.2 Simple non-repaired blocks . 89
C.3.3 Composite block: example on a non-repaired standby system . 89
C.4 RBD driven Markov processes . 91
C.5 Average and asymptotic (steady state) availability calculations . 92
C.6 Frequency calculations . 93
C.7 Reliability calculations . 94
Annex D (informative) Importance factors . 96
D.1 General . 96
D.2 Vesely-Fussell importance factor . 96
D.3 Birnbaum importance factor or marginal importance factor . 96
D.4 Lambert importance factor or critical importance factor . 97
D.5 Diagnostic importance factor . 97
D.6 Risk achievement worth . 98
D.7 Risk reduction worth . 98
D.8 Differential importance measure . 98
D.9 Remarks about importance factors . 99
Annex E (informative) RBD driven Petri nets . 100
E.1 General . 100
E.2 Example of sub-PN to be used within RBD driven PN models . 100
E.3 Evaluation of the DRBD state . 102
E.4 Availability, reliability, frequency and MTTF calculations . 104
Annex F (informative) Numerical examples and curves . 105
F.1 General . 105
F.2 Typical series RBD structure . 105
F.2.1 Non-repaired blocks . 105
F.2.2 Repaired blocks . 106
F.3 Typical parallel RBD structure . 107
F.3.1 Non-repaired blocks . 107
F.3.2 Repaired blocks . 108
F.4 Complex RBD structures . 109
F.4.1 Non series-parallel RBD structure . 109
F.4.2 Convergence to asymptotic values versus MTTR . 110
F.4.3 System with periodically tested components . 111
F.5 Dynamic RBD example . 113
F.5.1 Comparison between analytical and Monte Carlo simulation results . 113
F.5.2 Dynamic RBD example . 113
Bibliography . 116
Figure 1 – Shannon decomposition of a simple Boolean expression and resulting BDD . 18
Figure 2 – Series reliability block diagram . 25
Figure 3 – Parallel reliability block diagram . 26
IEC 61078:2016 © IEC 2016 – 5 –
Figure 4 – Parallel structure made of duplicated series sub-RBD . 26
Figure 5 – Series structure made of parallel reliability block diagram . 27
Figure 6 – General series-parallel reliability block diagram . 27
Figure 7 – Another type of general series-parallel reliability block diagram . 27
Figure 8 – 2 out of 3 redundancy . 28
Figure 9 – 3 out of 4 redundancy . 28
Figure 10 – Diagram not easily represented by series/parallel arrangement of blocks . 28
Figure 11 – Example of RBD implementing dependent blocks . 29
Figure 12 – Example of a composite block . 29
Figure 13 – Use of transfer gates and sub-RBDs . 30
Figure 14 – Analogy between a block and an electrical switch . 30
Figure 15 – Analogy with an electrical circuit . 31
Figure 16 – Example of minimal success path (tie set) . 31
Figure 17 – Example of minimal failure path (cut set) . 31
Figure 18 – Equivalent RBDs with minimal success paths . 32
Figure 19 – Equivalent RBDs with minimal cut sets . 33
Figure 20 – Link between a basic series structure and probability calculations . 33
Figure 21 – Link between a parallel structure and probability calculations . 34
Figure 22 – "Availability" Markov graph for a simple repaired block . 38
Figure 23 – Standby redundancy . 38
Figure 24 – Typical availability of a periodically tested block . 39
Figure 25 – Example of RBD reaching a steady state . 41
Figure 26 – Example of RBD with recurring phases . 41
Figure 27 – RBD and equivalent Markov graph for reliability calculations . 42
Figure 28 – Illustrating grouping of blocks before reduction . 44
Figure 29 – Reduced reliability block diagrams . 44
Figure 30 – Representation of Figure 10 when item A has failed . 45
Figure 31 – Representation of Figure 10 when item A is working . 45
Figure 32 – RBD representing three redundant items . 46
Figure 33 – Shannon decomposition equivalent to Table 5 . 49
Figure 34 – Binary decision diagram equivalent to Table 5 . 49
Figure 35 – RBD using an arrow to help define system success . 51
Figure 36 – Alternative representation of Figure 35 using repeated blocks and success
paths . 51
Figure 37 – Other alternative representation of Figure 35 using repeated blocks and
minimal cut sets . 52
Figure 38 – Shannon decomposition related to Figure 35 . 53
Figure 39 – 2-out-of-5 non-identical items . 54
Figure 40 – Direct and inverted block . 55
Figure 41 – Example of electrical circuit with a commutator A . 55
Figure 42 – Electrical circuit: failure paths . 55
Figure 43 – Example RBD with blocks with inverted states . 56
Figure 44 – BDD equivalent to Figure 43 . 57
Figure 45 – Symbol for external elements . 58
– 6 – IEC 61078:2016 © IEC 2016
Figure 46 – Dynamic interaction between a CCF and RBDs' blocks . 60
Figure 47 – Various ways to indicate dynamic interaction between blocks . 60
Figure 48 – Dynamic interaction between a single repair team and RBDs' blocks . 60
Figure 49 – Implementation of a PAND gate . 61
Figure 50 – Equivalent finite-state automaton and example of chronogram for a PAND gate . 61
Figure 51 – Implementation of a SEQ gate . 61
Figure 52 – Equivalent finite-state automaton and example of chronogram for a SEQ gate . 62
Figure B.1 – Examples of minimal tie sets (success paths) . 68
Figure B.2 – Examples of non-minimal tie sets (non minimal success paths) . 68
Figure B.3 – Examples of minimal cut sets . 69
Figure B.4 – Examples of non-minimal cut sets . 69
Figure B.5 – Example of RBD with tie and cut sets of various order . 70
Figure B.6 – Reminder of the RBD in Figure 35 . 82
Figure B.7 – Shannon decomposition of the Boolean function represented by Figure B.6 . 82
Figure B.8 – Identification of the parts which do not matter . 83
Figure B.9 – Simplification of the Shannon decomposition . 83
Figure B.10 – Binary decision diagram related to the RBD in Figure B.6 . 84
Figure B.11 – Obtaining success paths (tie sets) from an RBD . 84
Figure B.12 – Obtaining failure paths (cut sets) from an RBD . 85
Figure B.13 – Finding cut and tie sets from BDDs . 85
Figure B.14 – Probabilistic calculations from a BDD. 86
Figure B.15 – Calculation of conditional probabilities using BDDs . 87
Figure C.1 – Principle of time dependent availability calculations . 88
Figure C.2 – Principle of RBD driven Markov processes . 91
Figure C.3 – Typical availability of RBD with quickly repaired failures . 91
Figure C.4 – Example of simple multi-phase Markov process . 92
Figure C.5 – Typical availability of RBD with periodically tested failures . 92
Figure E.1 – Example of a sub-PN modelling a DRBD block . 100
Figure E.2 – Example of a sub-PN modelling a common cause failure . 101
Figure E.3 – Example of DRBD based on RBD driven PN . 101
Figure E.4 – Logical calculation of classical RBD structures . 102
Figure E.5 – Example of logical calculation for an n/m gate . 102
Figure E.6 – Example of sub-PN modelling a PAND gate with 2 inputs . 103
Figure E.7 – Example of the inhibition of the failure of a block . 104
Figure E.8 – Sub-PN for availability, reliability and frequency calculations . 104
Figure F.1 – Availability/reliability of a typical non-repaired series structure . 105
Figure F.2 – Failure rate and failure frequency related to Figure F.1 . 106
Figure F.3 – Equivalence of a non-repaired series structure to a single block . 106
Figure F.4 – Availability/reliability of a typical repaired series structure . 106
Figure F.5 – Failure rate and failure frequency related to Figure F.4 . 107
Figure F.6 – Availability/reliability of a typical non-repaired parallel structure . 107
Figure F.7 – Failure rate and failure frequency related to Figure F.6 . 108
Figure F.8 – Availability/reliability of a typical repaired parallel structure . 108
IEC 61078:2016 © IEC 2016 – 7 –
Figure F.9 – Vesely failure rate and failure frequency related to Figure F.8 . 109
Figure F.10 – Example 1 from 7.5.2 . 109
Figure F.11 – Failure rate and failure frequency related to Figure F.10 . 110
Figure F.12 – Impact of the MTTR on the convergence quickness . 111
Figure F.13 – System with periodically tested blocks . 112
Figure F.14 – Failure rate and failure frequency related to Figure F.13 . 112
Figure F.15 – Analytical versus Monte Carlo simulation results . 113
Figure F.16 – Impact of CCF and limited number of repair teams . 114
Figure F.17 – Markov graphs modelling the impact of the number of repair teams . 115
Figure F.18 – Approximation for two redundant blocks . 115
Table 1 – Acronyms used in IEC 61078 . 18
Table 2 – Symbols used in IEC 61078 . 19
Table 3 – Graphical representation of RBDs: Boolean structures . 21
Table 4 – Graphical representation of RBDs: non-Boolean structures/DRBD . 22
Table 5 – Application of truth table to the example of Figure 32 . 46
Table 6 – Karnaugh map related to Figure 10 when A is in up state . 48
Table 7 – Karnaugh map related to Figure 10 when A is in down state . 48
Table 8 – Karnaugh map related to Figure 35 . 53
Table A.1 – Example of equations for calculating the probability of success of basic
configurations . 63
Table F.1 – Impact of functional dependencies . 114
– 8 – IEC 61078:2016 © IEC 2016
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
RELIABILITY BLOCK DIAGRAMS
FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of
patent rights. IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 61078 has been prepared by IEC technical committee 56:
Dependability.
This third edition cancels and replaces the second edition published in 2006. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) the structure of the document has been entirely reconsidered, the title modified and the
content extended and improved to provide more information about availability, reliability
and failure frequency calculations;
b) Clause 3 has been extended and clauses have been introduced to describe the electrical
analogy, the "non-coherent" RBDs and the "dynamic" RBDs;
c) Annex B about Boolean algebra methods has been extended;
d) Annex C (Calculations of time dependent probabilities), Annex D (Importance factors),
Annex E (RBD driven Petri net models) and Annex F (Numerical examples and curves)
have been introduced.
IEC 61078:2016 © IEC 2016 – 9 –
The text of this standard is based on the following documents:
FDIS Report on voting
56/1685/FDIS 56/1694/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
The committee has decided that the contents of this publication will remain unchanged until
the stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data
related to the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
– 10 – IEC 61078:2016 © IEC 2016
INTRODUCTION
A reliability block diagram (RBD) is a pictorial representation of a system's successful
functioning. It shows the logical connection of (functioning) components (represented by
blocks) needed for successful operation of the system (hereafter referred to as “system
success”). Therefore an RBD is equivalent to a logical equation of Boolean variables and the
probabilistic calculations are primarily related to constant values of the block success/failure
probabilities.
Many different analytical methods of dependability analysis are available, of which the RBD is
one. Therefore, the purpose of each method and their individual or combined applicability in
evaluating the availability, reliability, failure frequency and other dependability measures as
may be applicable to a given system or component should be examined by the analyst prior to
deciding to use the RBD. Consideration should also be given to the results obtainable from
each method, data required to perform the analysis, complexity of analysis and other factors
identified in this standard.
Provided that the blocks in the RBD behave independently from each other and that the order
in which failures occur does not matter then the probabilistic calculations can be extended to
time dependent probabilistic calculations involving non-repaired as well as repaired blocks
(e.g. blocks representing non-repaired or repaired components). In this case three
dependability measures related to the system successful functioning have to be considered:
the reliability itself, R (t), but also the availability, A (t) and the failure frequency, w (t). While,
S S S
for systems involving repaired components, the calculations of A (t) or w (t) can be done
S S
quite straightforwardly, the calculation of R (t) implies systemic dependencies (see definition
S
3.34) which cannot be taken into account within the mathematical framework of RBDs.
Nevertheless, in particular cases, approximations of R (t) are available.
S
The RBD technique is linked to fault tree analysis [1] and to Markov techniques [2]:
• The underlying mathematics is the same for RBDs and fault tree analysis (FTA): when an
RBD is focused on system success, the FT is focused on system failure. It is always
possible to transform an RBD into an FT and vice versa. From a mathematical point of
view, RBD and FT models share dual logical expressions. Therefore, the mathematical
developments and the limitations are similar in both cases.
• When the availability A (t) of one block can be calculated by using an individual Markov
i
process [2] independent of the other blocks, this availability, A (t), can be used as input for
i
the calculations related to an RBD including this block. This approach where an RBD
provides the logic structure and Markov processes numerical values of the availabilities of
the blocks is called "RBD driven Markov processes".
For systems where the order of failures is to be taken into account, or where the repaired
blocks do not behave independently from each other or where the system reliability, R (t),
S
cannot be calculated by analytical methods, Monte Carlo simulation or other modelling
techniques, such as dynamic RBDs, Markov [2] or Petri net techniques [3], may be more
suitable.
_______________
Numbers in square brackets refer to the Bibliography.
IEC 61078:2016 © IEC 2016 – 11 –
RELIABILITY BLOCK DIAGRAMS
1 Scope
This International Standard describes:
• the requirements to apply when reliability block diagrams (RBDs) are used in
dependability analysis;
• the procedures for modelling the dependability of a system with reliability block diagrams;
• how to use RBDs for qualitative and quantitative analysis;
• the procedures for using the RBD model to calculate availability, failure frequency and
reliability measures for different types of systems with constant (or time dependent)
probabilities of blocks success/failure, and for non-repaired blocks or repaired blocks;
• some theoretical aspects and limitations in performing calculations for availability, failure
frequency and reliability measures;
• the relationships with fault tree analysis (see IEC 61025 [1]) and Markov techniques (see
IEC 61165 [2]).
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and
are indispensable for its application. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60050-192, International Electrotechnical Vocabulary – Part 192: Dependability
(available
...
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