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)

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)

General Information

Status
Published
Publication Date
11-Aug-2016
Technical Committee
Current Stage
PPUB - Publication issued
Completion Date
12-Aug-2016
Ref Project

Buy Standard

Standard
IEC 61078:2016 - Reliability block diagrams
English and French language
250 pages
sale 15% off
Preview
sale 15% off
Preview

Standards Content (sample)

IEC 61078
Edition 3.0 2016-08
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Reliability block diagrams
Diagrammes de fiabilité
IEC 61078:2016-08(en-fr)
---------------------- Page: 1 ----------------------
THIS PUBLICATION IS COPYRIGHT PROTECTED
Copyright © 2016 IEC, Geneva, Switzerland

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form

or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from

either IEC or IEC's member National Committee in the country of the requester. If you have any questions about IEC

copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or

your local IEC member National Committee for further information.

Droits de reproduction réservés. Sauf indication contraire, aucune partie de cette publication ne peut être reproduite

ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique, y compris la photocopie

et les microfilms, sans l'accord écrit de l'IEC ou du Comité national de l'IEC du pays du demandeur. Si vous avez des

questions sur le copyright de l'IEC ou si vous désirez obtenir des droits supplémentaires sur cette publication, utilisez

les coordonnées ci-après ou contactez le Comité national de l'IEC de votre pays de résidence.

IEC Central Office Tel.: +41 22 919 02 11
3, rue de Varembé Fax: +41 22 919 03 00
CH-1211 Geneva 20 info@iec.ch
Switzerland www.iec.ch
About the IEC

The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes

International Standards for all electrical, electronic and related technologies.
About IEC publications

The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the

latest edition, a corrigenda or an amendment might have been published.
IEC Catalogue - webstore.iec.ch/catalogue Electropedia - www.electropedia.org

The stand-alone application for consulting the entire The world's leading online dictionary of electronic and

bibliographical information on IEC International Standards, electrical terms containing 20 000 terms and definitions in

Technical Specifications, Technical Reports and other English and French, with equivalent terms in 15 additional

documents. Available for PC, Mac OS, Android Tablets and languages. Also known as the International Electrotechnical

iPad. Vocabulary (IEV) online.

IEC publications search - www.iec.ch/searchpub IEC Glossary - std.iec.ch/glossary

The advanced search enables to find IEC publications by a 65 000 electrotechnical terminology entries in English and

variety of criteria (reference number, text, technical French extracted from the Terms and Definitions clause of

committee,…). It also gives information on projects, replaced IEC publications issued since 2002. Some entries have been

and withdrawn publications. collected from earlier publications of IEC TC 37, 77, 86 and

CISPR.
IEC Just Published - webstore.iec.ch/justpublished

Stay up to date on all new IEC publications. Just Published IEC Customer Service Centre - webstore.iec.ch/csc

details all new publications released. Available online and If you wish to give us your feedback on this publication or

also once a month by email. need further assistance, please contact the Customer Service

Centre: csc@iec.ch.
A propos de l'IEC

La Commission Electrotechnique Internationale (IEC) est la première organisation mondiale qui élabore et publie des

Normes internationales pour tout ce qui a trait à l'électricité, à l'électronique et aux technologies apparentées.

A propos des publications IEC

Le contenu technique des publications IEC est constamment revu. Veuillez vous assurer que vous possédez l’édition la

plus récente, un corrigendum ou amendement peut avoir été publié.
Catalogue IEC - webstore.iec.ch/catalogue Electropedia - www.electropedia.org
Application autonome pour consulter tous les renseignements
Le premier dictionnaire en ligne de termes électroniques et
bibliographiques sur les Normes internationales,
électriques. Il contient 20 000 termes et définitions en anglais
Spécifications techniques, Rapports techniques et autres
et en français, ainsi que les termes équivalents dans 15
documents de l'IEC. Disponible pour PC, Mac OS, tablettes
langues additionnelles. Egalement appelé Vocabulaire
Android et iPad.
Electrotechnique International (IEV) en ligne.
Recherche de publications IEC - www.iec.ch/searchpub
Glossaire IEC - std.iec.ch/glossary

La recherche avancée permet de trouver des publications IEC 65 000 entrées terminologiques électrotechniques, en anglais

en utilisant différents critères (numéro de référence, texte, et en français, extraites des articles Termes et Définitions des

comité d’études,…). Elle donne aussi des informations sur les publications IEC parues depuis 2002. Plus certaines entrées

projets et les publications remplacées ou retirées. antérieures extraites des publications des CE 37, 77, 86 et

CISPR de l'IEC.
IEC Just Published - webstore.iec.ch/justpublished
Service Clients - webstore.iec.ch/csc
Restez informé sur les nouvelles publications IEC. Just

Published détaille les nouvelles publications parues. Si vous désirez nous donner des commentaires sur cette

Disponible en ligne et aussi une fois par mois par email. publication ou si vous avez des questions contactez-nous:

csc@iec.ch.
---------------------- Page: 2 ----------------------
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
---------------------- Page: 3 ----------------------
– 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

---------------------- Page: 4 ----------------------
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

---------------------- Page: 5 ----------------------
– 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

---------------------- Page: 6 ----------------------
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

---------------------- Page: 7 ----------------------
– 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 .....................................

...

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.