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BS EN 61078:2016

BS EN 61078:2016

$215.11

Reliability block diagrams

Published By Publication Date Number of Pages
BSI 2016 124
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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)

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PDF Pages PDF Title
6 English
CONTENTS
12 FOREWORD
14 INTRODUCTION
15 1 Scope
2 Normative references
3 Terms and definitions
22 4 Symbols and abbreviated terms
Figures
Figure 1 ā€“ Shannon decomposition of a simple Boolean expression and resulting BDD
Tables
Table 1 ā€“ Acronyms used in IECĀ 61078
23 Table 2 ā€“ Symbols used in IECĀ 61078
25 Table 3 ā€“ Graphical representation of RBDs: Boolean structures
26 5 Preliminary considerations, main assumptions, and limitations
5.1 General considerations
Table 4 ā€“ Graphical representation of RBDs: non-Boolean structures/DRBD
27 5.2 Pre-requisite/main assumptions
5.3 Limitations
28 6 Establishment of system success/failed states
6.1 General considerations
6.2 Detailed considerations
6.2.1 System operation
29 6.2.2 Environmental conditions
6.2.3 Duty cycles
7 Elementary models
7.1 Developing the model
7.2 Series structures
Figure 2 ā€“ Series reliability block diagram
30 7.3 Parallel structures
7.4 Mix of series and parallel structures
Figure 3 ā€“ Parallel reliability block diagram
Figure 4 ā€“ Parallel structure made of duplicated series sub-RBD
31 7.5 Other structures
7.5.1 m out of n structures
Figure 5 ā€“ Series structure made of parallel reliability block diagram
Figure 6 ā€“ General series-parallel reliability block diagram
Figure 7 ā€“ Another type of general series-parallel reliability block diagram
32 7.5.2 Structures with common blocks
Figure 8 ā€“ 2 out of 3 redundancy
Figure 9 ā€“ 3 out of 4 redundancy
Figure 10 ā€“ Diagram not easily represented by series/parallel arrangement of blocks
33 7.5.3 Composite blocks
7.6 Large RBDs and use of transfer gates
Figure 11 ā€“ Example of RBD implementing dependent blocks
Figure 12 ā€“ Example of a composite block
34 8 Qualitative analysis: minimal tie sets and minimal cut sets
8.1 Electrical analogy
Figure 13 ā€“ Use of transfer gates and sub-RBDs
Figure 14 ā€“ Analogy between a block and an electrical switch
35 Figure 15 ā€“ Analogy with an electrical circuit
Figure 16 ā€“ Example of minimal success path (tie set)
Figure 17 ā€“ Example of minimal failure path (cut set)
36 8.2 Series-parallel representation with minimal success path and cut sets
Figure 18 ā€“ Equivalent RBDs with minimal success paths
37 8.3 Qualitative analysis from minimal cut sets
9 Quantitative analysis: blocks with constant probability of failure/success
9.1 Series structures
Figure 19 ā€“ Equivalent RBDs with minimal cut sets
Figure 20 ā€“ Link between a basic series structure and probability calculations
38 9.2 Parallel structures
9.3 Mix of series and parallel structures
Figure 21 ā€“ Link between a parallel structure and probability calculations
39 9.4 m/n architectures (identical items)
10 Quantitative analysis: blocks with time dependent probabilities of failure/success
10.1 General
40 10.2 Non-repaired blocks
10.2.1 General
10.2.2 Simple non-repaired block
10.2.3 Non-repaired composite blocks
41 10.2.4 RBDs with non-repaired blocks
10.3 Repaired blocks
10.3.1 Availability calculations
42 Figure 22 ā€“ “Availability” Markov graph for a simple repaired block
Figure 23 ā€“ Standby redundancy
43 Figure 24 ā€“ Typical availability of a periodically tested block
44 10.3.2 Average availability calculations
45 Figure 25 ā€“ Example of RBD reaching a steady state
Figure 26 ā€“ Example of RBD with recurring phases
46 10.3.3 Reliability calculations
Figure 27 ā€“ RBD and equivalent Markov graph for reliability calculations
47 10.3.4 Frequency calculations
11 Boolean techniques for quantitative analysis of large models
11.1 General
48 11.2 Method of RBD reduction
Figure 28 ā€“ Illustrating grouping of blocks before reduction
Figure 29 ā€“ Reduced reliability block diagrams
49 11.3 Use of total probability theorem
Figure 30 ā€“ Representation of Figure 10 when item A has failed
Figure 31 ā€“ Representation of Figure 10 when item A is working
50 11.4 Use of Boolean truth tables
Figure 32 ā€“ RBD representing three redundant items
Table 5 ā€“ Application of truth table to the example of Figure 32
51 11.5 Use of Karnaugh maps
52 Table 6 ā€“ Karnaugh map related to Figure 10 when A is in up state
Table 7 ā€“ Karnaugh map related to Figure 10 when A is in down state
53 11.6 Use of the Shannon decomposition and binary decision diagrams
Figure 33 ā€“ Shannon decomposition equivalent to Table 5
Figure 34 ā€“ Binary decision diagram equivalent to Table 5
54 11.7 Use of Sylvester-PoincarƩ formula
55 11.8 Examples of RBD application
11.8.1 Models with repeated blocks
Figure 35 ā€“ RBD using an arrow to help define system success
Figure 36 ā€“ Alternative representation of Figure 35 using repeated blocks and success paths
56 Figure 37 ā€“ Other alternative representation of Figure 35 using repeated blocks and minimal cut sets
57 Figure 38 ā€“ Shannon decomposition related to Figure 35
Table 8 ā€“ Karnaugh map related to Figure 35
58 11.8.2 m out of n models (non-identical items)
12 Extension of reliability block diagram techniques
12.1 Non-coherent reliability block diagrams
Figure 39 ā€“ 2-out-of-5 non-identical items
59 Figure 40 ā€“ Direct and inverted block
Figure 41 ā€“ Example of electrical circuit with a commutator A
Figure 42 ā€“ Electrical circuit: failure paths
60 Figure 43 ā€“ Example RBD with blocks with inverted states
61 12.2 Dynamic reliability block diagrams
12.2.1 General
Figure 44 ā€“ BDD equivalent to Figure 43
62 12.2.2 Local interactions
Figure 45 ā€“ Symbol for external elements
63 12.2.3 Systemic dynamic interactions
12.2.4 Graphical representations of dynamic interactions
64 Figure 46 ā€“ Dynamic interaction between a CCF and RBDs’ blocks
Figure 47 ā€“ Various ways to indicate dynamic interaction between blocks
Figure 48 ā€“ Dynamic interaction between a single repair team and RBDs’ blocks
65 Figure 49 ā€“ Implementation of a PAND gate
Figure 50 ā€“ Equivalent finite-state automaton and exampleof chronogram for a PAND gate
Figure 51 ā€“ Implementation of a SEQ gate
66 12.2.5 Probabilistic calculations
Figure 52 ā€“ Equivalent finite-state automaton and exampleof chronogram for a SEQ gate
67 Annexes
Annex A (informative) Summary of formulae
Table A.1 ā€“ Example of equations for calculating the probability of success of basic configurations
71 Annex B (informative) Boolean algebra methods
B.1 Introductory remarks
B.2 Notation
72 B.3 Tie sets (success paths) and cut sets (failure paths) analysis
B.3.1 Notion of cut and tie sets
Figure B.1 ā€“ Examples of minimal tie sets (success paths)
Figure B.2 ā€“ Examples of non-minimal tie sets (non minimal success paths)
73 B.3.2 Series-parallel representation using minimal tie and cut sets
Figure B.3 ā€“ Examples of minimal cut sets
Figure B.4 ā€“ Examples of non-minimal cut sets
74 B.3.3 Identification of minimal cuts and tie sets
Figure B.5 ā€“ Example of RBD with tie and cut sets of various order
75 B.4 Principles of calculations
B.4.1 Series structures
B.4.2 Parallel structures
77 B.4.3 Mix of series and parallel structures
B.4.4 m out of n architectures (identical items)
78 B.5 Use of Sylvester-PoincarƩ formula for large RBDs and repeated blocks
B.5.1 General
B.5.2 Sylvester-PoincarƩ formula with tie sets
80 B.5.3 Sylvester-PoincarƩ formula with cut sets
81 B.6 Method for disjointing Boolean expressions
B.6.1 General and background
82 B.6.2 Disjointing principle
83 B.6.3 Disjointing procedure
B.6.4 Example of application of disjointing procedure
85 B.6.5 Comments
86 B.7 Binary decision diagrams
B.7.1 Establishing a BDD
Figure B.6 ā€“ Reminder of the RBD in Figure 35
Figure B.7 ā€“ Shannon decomposition of the Boolean function represented by Figure B.6
87 Figure B.8 ā€“ Identification of the parts which do not matter
Figure B.9 ā€“ Simplification of the Shannon decomposition
88 B.7.2 Minimal success paths and cut sets with BDDs
Figure B.10 ā€“ Binary decision diagram related to the RBD in Figure B.6
Figure B.11 ā€“ Obtaining success paths (tie sets) from an RBD
89 Figure B.12 ā€“ Obtaining failure paths (cut sets) from an RBD
Figure B.13 ā€“ Finding cut and tie sets from BDDs
90 B.7.3 Probabilistic calculations with BDDs
Figure B.14 ā€“ Probabilistic calculations from a BDD
91 B.7.4 Key remarks about the use of BDDs
Figure B.15 ā€“ Calculation of conditional probabilities using BDDs
92 Annex C (informative) Time dependent probabilities and RBD driven Markov processes
C.1 General
C.2 Principle for calculation of time dependent availabilities
Figure C.1 ā€“ Principle of time dependent availability calculations
93 C.3 Non-repaired blocks
C.3.1 General
C.3.2 Simple non-repaired blocks
C.3.3 Composite block: example on a non-repaired standby system
95 C.4 RBD driven Markov processes
Figure C.2 ā€“ Principle of RBD driven Markov processes
Figure C.3 ā€“ Typical availability of RBD with quickly repaired failures
96 C.5 Average and asymptotic (steady state) availability calculations
Figure C.4 ā€“ Example of simple multi-phase Markov process
Figure C.5 ā€“ Typical availability of RBD with periodically tested failures
97 C.6 Frequency calculations
98 C.7 Reliability calculations
100 Annex D (informative) Importance factors
D.1 General
D.2 Vesely-Fussell importance factor
D.3 Birnbaum importance factor or marginal importance factor
101 D.4 Lambert importance factor or critical importance factor
D.5 Diagnostic importance factor
102 D.6 Risk achievement worth
D.7 Risk reduction worth
D.8 Differential importance measure
103 D.9 Remarks about importance factors
104 Annex E (informative) RBD driven Petri nets
E.1 General
E.2 Example of sub-PN to be used within RBD driven PN models
Figure E.1 ā€“ Example of a sub-PN modelling a DRBD block
105 Figure E.2 ā€“ Example of a sub-PN modelling a common cause failure
Figure E.3 ā€“ Example of DRBD based on RBD driven PN
106 E.3 Evaluation of the DRBD state
Figure E.4 ā€“ Logical calculation of classical RBD structures
Figure E.5 ā€“ Example of logical calculation for an n/m gate
107 Figure E.6 ā€“ Example of sub-PN modelling a PAND gate with 2 inputs
108 E.4 Availability, reliability, frequency and MTTF calculations
Figure E.7 ā€“ Example of the inhibition of the failure of a block
Figure E.8 ā€“ Sub-PN for availability, reliability and frequency calculations
109 Annex F (informative) Numerical examples and curves
F.1 General
F.2 Typical series RBD structure
F.2.1 Non-repaired blocks
Figure F.1 ā€“ Availability/reliability of a typical non-repaired series structure
110 F.2.2 Repaired blocks
Figure F.2 ā€“ Failure rate and failure frequency related to Figure F.1
Figure F.3 ā€“ Equivalence of a non-repaired series structure to a single block
Figure F.4 ā€“ Availability/reliability of a typical repaired series structure
111 F.3 Typical parallel RBD structure
F.3.1 Non-repaired blocks
Figure F.5 ā€“ Failure rate and failure frequency related to Figure F.4
Figure F.6 ā€“ Availability/reliability of a typical non-repaired parallel structure
112 F.3.2 Repaired blocks
Figure F.7 ā€“ Failure rate and failure frequency related to Figure F.6
Figure F.8 ā€“ Availability/reliability of a typical repaired parallel structure
113 F.4 Complex RBD structures
F.4.1 Non series-parallel RBD structure
Figure F.9 ā€“ Vesely failure rate and failure frequency related to Figure F.8
Figure F.10 ā€“ Example 1 from 7.5.2
114 F.4.2 Convergence to asymptotic values versus MTTR
Figure F.11 ā€“ Failure rate and failure frequency related to Figure F.10
115 F.4.3 System with periodically tested components
Figure F.12 ā€“ Impact of the MTTR on the convergence quickness
116 Figure F.13 ā€“ System with periodically tested blocks
Figure F.14 ā€“ Failure rate and failure frequency related to Figure F.13
117 F.5 Dynamic RBD example
F.5.1 Comparison between analytical and Monte Carlo simulation results
F.5.2 Dynamic RBD example
Figure F.15 ā€“ Analytical versus Monte Carlo simulation results
118 Figure F.16 ā€“ Impact of CCF and limited number of repair teams
Table F.1 ā€“ Impact of functional dependencies
119 Figure F.17 ā€“ Markov graphs modelling the impact of the number of repair teams
Figure F.18 ā€“ Approximation for two redundant blocks
120 Bibliography

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