1、EIASTANDARDReality Block DiagramsEIA-61078 (IEC 61078:2016, IDT) January 2018 Electronic Components Industry Association ANSI/EIA-61078-2018 Approved: January 17, 2018EIA-61078NOTICEEIA Engineering Standards and Publications are designed to serve the public interest through eliminating misunderstand
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4、or internationally. Standards and Publications are adopted by ECIA in accordance with the American National Standards Institute (ANSI) patent policy. By such action, ECIA does not assume any liability to any patent owner, nor does it assume any obligation whatever to parties adopting the Standard or
5、 Publication. This EIA Standard is identical (IDT) with the International Standard IEC Publication 61078:2016 Edition 3: Reliability Block Diagrams. This document is the EIA Standard EIA-61078-2018 Edition 1: Reliability Block Diagrams. The text, figures and tables of IEC 61078:2018 are used in this
6、 Standard with the consent of the IEC and the American National Standards Institute (ANSI). The IEC copyrighted material has been reproduced with permission from ANSI. The IEC Foreword and Introduction are not part of the requirements of this standard but are included for information purposes only.
7、This Standard does not purport to address all safety problems associated with its use or all applicable regulatory requirements. It is the responsibility of the user of this Standard to establish appropriate safety and health practices and to determine the applicability of regulatory limitations bef
8、ore its use. (From Standards Proposal No. 5398, formulated under the cognizance of the Committee for Dependability Standards.Published by Electronic Components Industry Association 2018 Engineering Department 2214 Rock Hill Road, Suite 265 Herndon, VA 20170 PLEASE ! DONT VIOLATE THE LAW!This documen
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10、 (1-877-413-5186), International (303-397-7956) i CONTENTS FOREWORD . viiINTRODUCTION ix1 Scope 12 Normative references 13 Terms and definitions 14 Symbols and abbreviated terms . 85 Preliminary considerations, main assumptions, and limitations 125.1 General considerations . 125.2 Pre-requisite/main
11、 assumptions 135.3 Limitations 136 Establishment of system success/failed states . 146.1 General considerations . 146.2 Detailed considerations . 146.2.1 System operation . 146.2.2 Environmental conditions . 156.2.3 Duty cycles 157 Elementary models 157.1 Developing the model . 157.2 Series structur
12、es . 157.3 Parallel structures . 167.4 Mix of series and parallel structures 167.5 Other structures 177.5.1 m out of n structures 177.5.2 Structures with common blocks 187.5.3 Composite blocks 197.6 Large RBDs and use of transfer gates . 198 Qualitative analysis: minimal tie sets and minimal cut set
13、s. . 208.1 Electrical analogy 208.2 Series-parallel representation with minimal success path and cut sets 228.3 Qualitative analysis from minimal cut sets . 239 Quantitative analysis: blocks with constant probability of failure/success . 239.1 Series structures . 239.2 Parallel structures . 249.3 Mi
14、x of series and parallel structures 249.4 m/n architectures (identical items) . 2410 Quantitative analysis: blocks with time dependent probabilities of failure/success . 2510.1 General . 2510.2 Non-repaired blocks 2610.2.1 General . 2610.2.2 Simple non-repaired block . 2610.2.3 Non-repaired composit
15、e blocks 2610.2.4 RBDs with non-repaired blocks 2710.3 Repaired blocks 2710.3.1 Availability calculations 2710.3.2 Average availability calculations 29ii 10.3.3 Reliability calculations . 3110.3.4 Frequency calculations 3311 Boolean techniques for quantitative analysis of large models . 3311.1 Gener
16、al . 3311.2 Method of RBD reduction 3311.3 Use of total probability theorem. 3411.4 Use of Boolean truth tables . 3511.5 Use of Karnaugh maps 3711.6 Use of the Shannon decomposition and binary decision diagrams . 3811.7 Use of Sylvester-Poincar formula 3911.8 Examples of RBD application 4111.8.1 Mod
17、els with repeated blocks 4111.8.2 m out of n models (non-identical items) 4312 Extension of reliability block diagram techniques . 4412.1 Non-coherent reliability block diagrams . 4412.2 Dynamic reliability block diagrams 4612.2.1 General . 4612.2.2 Local interactions 4712.2.3 Systemic dynamic inter
18、actions . 4812.2.4 Graphical representations of dynamic interactions . 4912.2.5 Probabilistic calculations . 52Annex A (informative) Summary of formulae 53Annex B (informative) Boolean algebra methods 57B.1 Introductory remarks . 57B.2 Notation 57B.3 Tie sets (success paths) and cut sets (failure pa
19、ths) analysis . 58B.3.1 Notion of cut and tie sets . 58B.3.2 Series-parallel representation using minimal tie and cut sets . 59B.3.3 Identification of minimal cuts and tie sets . 60B.4 Principles of calculations . 61B.4.1 Series structures . 61B.4.2 Parallel structures 61B.4.3 Mix of series and para
20、llel structures . 63B.4.4 m out of n architectures (identical items) 63B.5 Use of Sylvester Poincar formula for large RBDs and repeated blocks 64B.5.1 General . 64B.5.2 Sylvester Poincar formula with tie sets . 64B.5.3 Sylvester Poincar formula with cut sets 66B.6 Method for disjointing Boolean expr
21、essions 67B.6.1 General and background 67B.6.2 Disjointing principle . 68B.6.3 Disjointing procedure . 69B.6.4 Example of application of disjointing procedure . 69B.6.5 Comments . 71B.7 Binary decision diagrams 71B.7.1 Establishing a BDD 71B.7.2 Minimal success paths and cut sets with BDDs 74B.7.3 P
22、robabilistic calculations with BDDs 76iii B.7.4 Key remarks about the use of BDDs 77Annex C (informative) Time dependent probabilities and RBD driven Markov processes . 78C.1 General . 78C.2 Principle for calculation of time dependent availabilities 78C.3 Non-repaired blocks 79C.3.1 General . 79C.3.
23、2 Simple non-repaired blocks 79C.3.3 Composite block: example on a non-repaired standby system . 79C.4 RBD driven Markov processes 81C.5 Average and asymptotic (steady state) availability calculations . 82C.6 Frequency calculations . 83C.7 Reliability calculations . 84Annex D (informative) Importanc
24、e factors 86D.1 General . 86D.2 Vesely-Fussell importance factor 86D.3 Birnbaum importance factor or marginal importance factor 86D.4 Lambert importance factor or critical importance factor . 87D.5 Diagnostic importance factor . 87D.6 Risk achievement worth 88D.7 Risk reduction worth . 88D.8 Differe
25、ntial importance measure 88D.9 Remarks about importance factors 89Annex E (informative) RBD driven Petri nets 90E.1 General . 90E.2 Example of sub-PN to be used within RBD driven PN models . 90E.3 Evaluation of the DRBD state 92E.4 Availability, reliability, frequency and MTTF calculations . 93Annex
26、 F (informative) Numerical examples and curves 95F.1 General . 95F.2 Typical series RBD structure . 95F.2.1 Non-repaired blocks . 95F.2.2 Repaired blocks . 96F.3 Typical parallel RBD structure . 97F.3.1 Non-repaired blocks . 97F.3.2 Repaired blocks . 98F.4 Complex RBD structures . 99F.4.1 Non series
27、-parallel RBD structure 99F.4.2 Convergence to asymptotic values versus MTTR . 100F.4.3 System with periodically tested components 101F.5 Dynamic RBD example . 102F.5.1 Comparison between analytical and Monte Carlo simulation results . 102F.5.2 Dynamic RBD example 102Bibliography 105Figure 1 Shannon
28、 decomposition of a simple Boolean expression and resulting BDD 8Figure 2 Series reliability block diagram . 15Figure 3 Parallel reliability block diagram . 16iv Figure 4 Parallel structure made of duplicated series sub-RBD 16Figure 5 Series structure made of parallel reliability block diagram 17Fig
29、ure 6 General series-parallel reliability block diagram . 17Figure 7 Another type of general series-parallel reliability block diagram . 17Figure 8 2 out of 3 redundancy 18Figure 9 3 out of 4 redundancy 18Figure 10 Diagram not easily represented by series/parallel arrangement of blocks . 18Figure 11
30、 Example of RBD implementing dependent blocks . 19Figure 12 Example of a composite block 19Figure 13 Use of transfer gates and sub-RBDs 19Figure 14 Analogy between a block and an electrical switch 20Figure 15 Analogy with an electrical circuit 20Figure 16 Example of minimal success path (tie set) 21
31、Figure 17 Example of minimal failure path (cut set) 21Figure 18 Equivalent RBDs with minimal success paths . 22Figure 19 Equivalent RBDs with minimal cut sets . 22Figure 20 Link between a basic series structure and probability calculations 23Figure 21 Link between a parallel structure and probabilit
32、y calculations . 24Figure 22 “Availability“ Markov graph for a simple repaired block . 28Figure 23 Standby redundancy . 28Figure 24 Typical availability of a periodically tested block . 29Figure 25 Example of RBD reaching a steady state 30Figure 26 Example of RBD with recurring phases . 31Figure 27
33、RBD and equivalent Markov graph for reliability calculations 32Figure 28 Illustrating grouping of blocks before reduction. 34Figure 29 Reduced reliability block diagrams . 34Figure 30 Representation of Figure 10 when item A has failed . 35Figure 31 Representation of Figure 10 when item A is working
34、35Figure 32 RBD representing three redundant items 35Figure 33 Shannon decomposition equivalent to Table 5 39Figure 34 Binary decision diagram equivalent to Table 5 39Figure 35 RBD using an arrow to help define system success 41Figure 36 Alternative representation of Figure 35 using repeated blocks
35、and success paths 41Figure 37 Other alternative representation of Figure 35 using repeated blocks and minimal cut sets 41Figure 38 Shannon decomposition related to Figure 35 43Figure 39 2-out-of-5 non-identical items . 43Figure 40 Direct and inverted block 44Figure 41 Example of electrical circuit w
36、ith a commutator A . 44Figure 42 Electrical circuit: failure paths. 45Figure 43 Example RBD with blocks with inverted states 45Figure 44 BDD equivalent to Figure 43. 46v Figure 45 Symbol for external elements . 47Figure 46 Dynamic interaction between a CCF and RBDs blocks 49Figure 47 Various ways to
37、 indicate dynamic interaction between blocks . 49Figure 48 Dynamic interaction between a single repair team and RBDs blocks 50Figure 49 Implementation of a PAND gate . 50Figure 50 Equivalent finite-state automaton and example of chronogram for a PAND gate . 51Figure 51 Implementation of a SEQ gate 5
38、1Figure 52 Equivalent finite-state automaton and example of chronogram for a SEQ gate . 51Figure B.1 Examples of minimal tie sets (success paths) . 58Figure B.2 Examples of non-minimal tie sets (non minimal success paths) . 58Figure B.3 Examples of minimal cut sets 59Figure B.4 Examples of non-minim
39、al cut sets . 59Figure B.5 Example of RBD with tie and cut sets of various order 60Figure B.6 Reminder of the RBD in Figure 35. 72Figure B.7 Shannon decomposition of the Boolean function represented by Figure B.6 72Figure B.8 Identification of the parts which do not matter . 73Figure B.9 Simplificat
40、ion of the Shannon decomposition 73Figure B.10 Binary decision diagram related to the RBD in Figure B.6 . 74Figure B.11 Obtaining success paths (tie sets) from an RBD 74Figure B.12 Obtaining failure paths (cut sets) from an RBD 75Figure B.13 Finding cut and tie sets from BDDs . 75Figure B.14 Probabi
41、listic calculations from a BDD 76Figure B.15 Calculation of conditional probabilities using BDDs . 77Figure C.1 Principle of time dependent availability calculations 78Figure C.2 Principle of RBD driven Markov processes 81Figure C.3 Typical availability of RBD with quickly repaired failures . 81Figu
42、re C.4 Example of simple multi-phase Markov process 82Figure C.5 Typical availability of RBD with periodically tested failures . 82Figure E.1 Example of a sub-PN modelling a DRBD block 90Figure E.2 Example of a sub-PN modelling a common cause failure 91Figure E.3 Example of DRBD based on RBD driven
43、PN . 91Figure E.4 Logical calculation of classical RBD structures . 92Figure E.5 Example of logical calculation for an n/m gate . 92Figure E.6 Example of sub-PN modelling a PAND gate with 2 inputs 92Figure E.7 Example of the inhibition of the failure of a block 93Figure E.8 Sub-PN for availability,
44、reliability and frequency calculations 94Figure F.1 Availability/reliability of a typical non-repaired series structure 95Figure F.2 Failure rate and failure frequency related to Figure F.1 . 96Figure F.3 Equivalence of a non-repaired series structure to a single block . 96Figure F.4 Availability/re
45、liability of a typical repaired series structure . 96Figure F.5 Failure rate and failure frequency related to Figure F.4 . 97Figure F.6 Availability/reliability of a typical non-repaired parallel structure 97Figure F.7 Failure rate and failure frequency related to Figure F.6 . 98vi Figure F.8 Availa
46、bility/reliability of a typical repaired parallel structure . 98Figure F.9 Vesely failure rate and failure frequency related to Figure F.8 . 99Figure F.10 Example 1 from 7.5.2 99Figure F.11 Failure rate and failure frequency related to Figure F.10 . 100Figure F.12 Impact of the MTTR on the convergen
47、ce quickness . 100Figure F.13 System with periodically tested blocks 101Figure F.14 Failure rate and failure frequency related to Figure F.13 . 102Figure F.15 Analytical versus Monte Carlo simulation results . 102Figure F.16 Impact of CCF and limited number of repair teams 103Figure F.17 Markov grap
48、hs modelling the impact of the number of repair teams. 104Figure F.18 Approximation for two redundant blocks 104Table 1 Acronyms used in IEC 61078. 8Table 2 Symbols used in IEC 61078 . 9Table 3 Graphical representation of RBDs: Boolean structures 11Table 4 Graphical representation of RBDs: non-Boole
49、an structures/DRBD . 12Table 5 Application of truth table to the example of Figure 32 36Table 6 Karnaugh map related to Figure 10 when A is in up state 37Table 7 Karnaugh map related to Figure 10 when A is in down state 37Table 8 Karnaugh map related to Figure 35 . 42Table A.1 Example of equations for calculating the probability of success of basic configurations . 53Table F
