1、Reliability block diagramsBS EN 61078:2016BSI Standards PublicationWB11885_BSI_StandardCovs_2013_AW.indd 1 15/05/2013 15:06National forewordThis British Standard is the UK implementation of EN 61078:2016. It is identical to IEC 61078:2016. It supersedes BS EN 61078:2006 which willbe withdrawn on 16
2、September 2019.The UK participation in its preparation was entrusted to TechnicalCommittee DS/1, Dependability.A list of organizations represented on this committee can be obtained onrequest to its secretary.This publication does not purport to include all the necessary provisions ofa contract. User
3、s are responsible for its correct application. The British Standards Institution 2016.Published by BSI Standards Limited 2016ISBN 978 0 580 87533 5ICS 03.120.01; 03.120.99Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the aut
4、hority of theStandards Policy and Strategy Committee on 31 December 2016.Amendments/corrigenda issued since publicationDate Text affectedBRITISH STANDARDBS EN 61078:2016EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN 61078 November 2016 ICS 03.120.01; 03.120.99 Supersedes EN 61078:2006 English
5、Version Reliability block diagrams (IEC 61078:2016) Diagrammes de fiabilit (IEC 61078:2016) Zuverlssigkeitsblockdiagramme (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 c
6、onditions 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 Standar
7、d 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 th
8、e 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, Polan
9、d, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. European Committee for Electrotechnical Standardization Comit Europen de Normalisation Electrotechnique Europisches Komitee fr Elektrotechnische Normung CEN-CENELEC Management Centre: Avenue Marnix 1
10、7, 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 BS EN 61078:2016EN 61078:2016 2 European foreword The text of document 56/1685/FDIS, future edition 3 of IEC 61078, prepared by IEC/TC 56 “Dependab
11、ility“ was submitted to the IEC-CENELEC parallel vote and approved by CENELEC as EN 61078:2016. The following dates are fixed: latest date by which the document has to be implemented at national level by publication of an identical national standard or by endorsement (dop) 2017-06-16 latest date by
12、which the national standards conflicting with the document have to be withdrawn (dow) 2019-09-16 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 responsi
13、ble 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 indic
14、ated: 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
15、 NOTE Harmonized as CEN ISO/TR 12489. BS EN 61078:2016EN 61078:2016 3 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
16、 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 E
17、N/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 expre
18、ssions for reliability, availability, maintainability and maintenance support terms EN 61703 - BS EN 61078:2016 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 consid
19、erations, 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
20、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 Composit
21、e 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 anal
22、ysis: 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.
23、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 BS EN 61078:
24、2016IEC 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
25、.5 Use of Karnaugh maps 47 11.6 Use of the Shannon decomposition and binary decision diagrams 49 11.7 Use of Sylvester-Poincar 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
26、 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
27、 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 m
28、inimal 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 Po
29、incar formula for large RBDs and repeated blocks 74 B.5.1 General . 74 B.5.2 Sylvester Poincar formula with tie sets 74 B.5.3 Sylvester Poincar 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 Disjoint
30、ing 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 BS EN 61078:2016 4 IEC 61078:2016 IEC
31、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 block
32、s 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 Gene
33、ral . 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 importa
34、nce 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
35、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 . 1
36、09 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 Biblio
37、graphy . 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 BS EN 61078:2016IEC 61078:2016 IEC 2016 5 Figure 4 Parallel structure made of duplicated series sub-RBD . 26
38、 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 Dia
39、gram 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 An
40、alogy 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 str
41、ucture 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 Examp
42、le 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 Representatio
43、n 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 a
44、n 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 Figu
45、re 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 Figu
46、re 45 Symbol for external elements 58 BS EN 61078:2016 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 Fig
47、ure 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 se
48、ts (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
49、 . 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) fro
