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 [1]) and Markov techniques (see
IEC 61165 [2]).

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

Status
Published
Publication Date
08-Dec-2016
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
30-Nov-2016
Due Date
04-Feb-2017
Completion Date
09-Dec-2016

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SLOVENSKI STANDARD
SIST EN 61078:2017
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
SIST EN 61078:2017 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 61078:2017
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SIST EN 61078:2017
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
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SIST EN 61078:2017
EN 61078:2016
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.
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SIST EN 61078:2017
EN 61078:2016
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
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SIST EN 61078:2017
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SIST EN 61078:2017
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

Warning! Make sure that you obtained this publication from an authorized distributor.

Attention! Veuillez vous assurer que vous avez obtenu cette publication via un distributeur agréé.

® Registered trademark of the International Electrotechnical Commission
Marque déposée de la Commission Electrotechnique Internationale
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SIST EN 61078:2017
– 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

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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

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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

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SIST EN 61078:2017
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

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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
...

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