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19、NATIONALE Reliability block diagrams Diagrammes de fiabilit INTERNATIONAL ELECTROTECHNICAL COMMISSION COMMISSION ELECTROTECHNIQUE INTERNATIONALE ICS 03.120.01; 03.120.99 ISBN 978-2-8322-3561-4 Registered trademark of the International Electrotechnical Commission Marque dpose de la Commission Electro
20、technique Internationale 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 agr. 2 IEC 61078:2016 IEC 2016 CONTENTS FOREWORD . 8 INTRODUCTION . 10 1 Scope 11 2 Normative ref
21、erences. 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 con
22、siderations 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 stru
23、ctures 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 su
24、ccess 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) 3
25、5 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 3
26、7 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.
27、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-Poincar formula . 50 11.8 Examples of RBD application. 51 11.8.1 Models with repeated blocks 51 11.8.
28、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 Graphi
29、cal 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
30、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 .
31、73 B.4.4 m out of n architectures (identical items) . 73 B.5 Use of Sylvester Poincar 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 .
32、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
33、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-repair
34、ed 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 calculati
35、ons . 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 achievemen
36、t 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 Availa
37、bility, 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 .
38、 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 Carl
39、o 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 s
40、tructure 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 Fi
41、gure 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
42、 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 se
43、ts 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
44、 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 reliab
45、ility 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 e
46、quivalent 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 Shann
47、on 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
48、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
49、 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 E
