{"id":344656,"date":"2024-10-20T00:12:36","date_gmt":"2024-10-20T00:12:36","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/bs-en-610782016-tc\/"},"modified":"2024-10-25T23:35:45","modified_gmt":"2024-10-25T23:35:45","slug":"bs-en-610782016-tc","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/bsi\/bs-en-610782016-tc\/","title":{"rendered":"BS EN 61078:2016 – TC"},"content":{"rendered":"

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)<\/p>\n

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PDF Pages<\/th>\nPDF Title<\/th>\n<\/tr>\n
174<\/td>\nEnglish
CONTENTS <\/td>\n<\/tr>\n
180<\/td>\nFOREWORD <\/td>\n<\/tr>\n
182<\/td>\nINTRODUCTION <\/td>\n<\/tr>\n
183<\/td>\n1 Scope
2 Normative references
3 Terms and definitions <\/td>\n<\/tr>\n
190<\/td>\n4 Symbols and abbreviated terms
Figures
Figure 1 \u2013 Shannon decomposition of a simple Boolean expression and resulting BDD
Tables
Table 1 \u2013 Acronyms used in IEC\u00a061078 <\/td>\n<\/tr>\n
191<\/td>\nTable 2 \u2013 Symbols used in IEC\u00a061078 <\/td>\n<\/tr>\n
193<\/td>\nTable 3 \u2013 Graphical representation of RBDs: Boolean structures <\/td>\n<\/tr>\n
194<\/td>\n5 Preliminary considerations, main assumptions, and limitations
5.1 General considerations
Table 4 \u2013 Graphical representation of RBDs: non-Boolean structures\/DRBD <\/td>\n<\/tr>\n
195<\/td>\n5.2 Pre-requisite\/main assumptions
5.3 Limitations <\/td>\n<\/tr>\n
196<\/td>\n6 Establishment of system success\/failed states
6.1 General considerations
6.2 Detailed considerations
6.2.1 System operation <\/td>\n<\/tr>\n
197<\/td>\n6.2.2 Environmental conditions
6.2.3 Duty cycles
7 Elementary models
7.1 Developing the model
7.2 Series structures
Figure 2 \u2013 Series reliability block diagram <\/td>\n<\/tr>\n
198<\/td>\n7.3 Parallel structures
7.4 Mix of series and parallel structures
Figure 3 \u2013 Parallel reliability block diagram
Figure 4 \u2013 Parallel structure made of duplicated series sub-RBD <\/td>\n<\/tr>\n
199<\/td>\n7.5 Other structures
7.5.1 m out of n structures
Figure 5 \u2013 Series structure made of parallel reliability block diagram
Figure 6 \u2013 General series-parallel reliability block diagram
Figure 7 \u2013 Another type of general series-parallel reliability block diagram <\/td>\n<\/tr>\n
200<\/td>\n7.5.2 Structures with common blocks
Figure 8 \u2013 2 out of 3 redundancy
Figure 9 \u2013 3 out of 4 redundancy
Figure 10 \u2013 Diagram not easily represented by series\/parallel arrangement of blocks <\/td>\n<\/tr>\n
201<\/td>\n7.5.3 Composite blocks
7.6 Large RBDs and use of transfer gates
Figure 11 \u2013 Example of RBD implementing dependent blocks
Figure 12 \u2013 Example of a composite block <\/td>\n<\/tr>\n
202<\/td>\n8 Qualitative analysis: minimal tie sets and minimal cut sets
8.1 Electrical analogy
Figure 13 \u2013 Use of transfer gates and sub-RBDs
Figure 14 \u2013 Analogy between a block and an electrical switch <\/td>\n<\/tr>\n
203<\/td>\nFigure 15 \u2013 Analogy with an electrical circuit
Figure 16 \u2013 Example of minimal success path (tie set)
Figure 17 \u2013 Example of minimal failure path (cut set) <\/td>\n<\/tr>\n
204<\/td>\n8.2 Series-parallel representation with minimal success path and cut sets
Figure 18 \u2013 Equivalent RBDs with minimal success paths <\/td>\n<\/tr>\n
205<\/td>\n8.3 Qualitative analysis from minimal cut sets
9 Quantitative analysis: blocks with constant probability of failure\/success
9.1 Series structures
Figure 19 \u2013 Equivalent RBDs with minimal cut sets
Figure 20 \u2013 Link between a basic series structure and probability calculations <\/td>\n<\/tr>\n
206<\/td>\n9.2 Parallel structures
9.3 Mix of series and parallel structures
Figure 21 \u2013 Link between a parallel structure and probability calculations <\/td>\n<\/tr>\n
207<\/td>\n9.4 m\/n architectures (identical items)
10 Quantitative analysis: blocks with time dependent probabilities of failure\/success
10.1 General <\/td>\n<\/tr>\n
208<\/td>\n10.2 Non-repaired blocks
10.2.1 General
10.2.2 Simple non-repaired block
10.2.3 Non-repaired composite blocks <\/td>\n<\/tr>\n
209<\/td>\n10.2.4 RBDs with non-repaired blocks
10.3 Repaired blocks
10.3.1 Availability calculations <\/td>\n<\/tr>\n
210<\/td>\nFigure 22 \u2013 “Availability” Markov graph for a simple repaired block
Figure 23 \u2013 Standby redundancy <\/td>\n<\/tr>\n
211<\/td>\nFigure 24 \u2013 Typical availability of a periodically tested block <\/td>\n<\/tr>\n
212<\/td>\n10.3.2 Average availability calculations <\/td>\n<\/tr>\n
213<\/td>\nFigure 25 \u2013 Example of RBD reaching a steady state
Figure 26 \u2013 Example of RBD with recurring phases <\/td>\n<\/tr>\n
214<\/td>\n10.3.3 Reliability calculations
Figure 27 \u2013 RBD and equivalent Markov graph for reliability calculations <\/td>\n<\/tr>\n
215<\/td>\n10.3.4 Frequency calculations
11 Boolean techniques for quantitative analysis of large models
11.1 General <\/td>\n<\/tr>\n
216<\/td>\n11.2 Method of RBD reduction
Figure 28 \u2013 Illustrating grouping of blocks before reduction
Figure 29 \u2013 Reduced reliability block diagrams <\/td>\n<\/tr>\n
217<\/td>\n11.3 Use of total probability theorem
Figure 30 \u2013 Representation of Figure 10 when item A has failed
Figure 31 \u2013 Representation of Figure 10 when item A is working <\/td>\n<\/tr>\n
218<\/td>\n11.4 Use of Boolean truth tables
Figure 32 \u2013 RBD representing three redundant items
Table 5 \u2013 Application of truth table to the example of Figure 32 <\/td>\n<\/tr>\n
219<\/td>\n11.5 Use of Karnaugh maps <\/td>\n<\/tr>\n
220<\/td>\nTable 6 \u2013 Karnaugh map related to Figure 10 when A is in up state
Table 7 \u2013 Karnaugh map related to Figure 10 when A is in down state <\/td>\n<\/tr>\n
221<\/td>\n11.6 Use of the Shannon decomposition and binary decision diagrams
Figure 33 \u2013 Shannon decomposition equivalent to Table 5
Figure 34 \u2013 Binary decision diagram equivalent to Table 5 <\/td>\n<\/tr>\n
222<\/td>\n11.7 Use of Sylvester-Poincar\u00e9 formula <\/td>\n<\/tr>\n
223<\/td>\n11.8 Examples of RBD application
11.8.1 Models with repeated blocks
Figure 35 \u2013 RBD using an arrow to help define system success
Figure 36 \u2013 Alternative representation of Figure 35 using repeated blocks and success paths <\/td>\n<\/tr>\n
224<\/td>\nFigure 37 \u2013 Other alternative representation of Figure 35 using repeated blocks and minimal cut sets <\/td>\n<\/tr>\n
225<\/td>\nFigure 38 \u2013 Shannon decomposition related to Figure 35
Table 8 \u2013 Karnaugh map related to Figure 35 <\/td>\n<\/tr>\n
226<\/td>\n11.8.2 m out of n models (non-identical items)
12 Extension of reliability block diagram techniques
12.1 Non-coherent reliability block diagrams
Figure 39 \u2013 2-out-of-5 non-identical items <\/td>\n<\/tr>\n
227<\/td>\nFigure 40 \u2013 Direct and inverted block
Figure 41 \u2013 Example of electrical circuit with a commutator A
Figure 42 \u2013 Electrical circuit: failure paths <\/td>\n<\/tr>\n
228<\/td>\nFigure 43 \u2013 Example RBD with blocks with inverted states <\/td>\n<\/tr>\n
229<\/td>\n12.2 Dynamic reliability block diagrams
12.2.1 General
Figure 44 \u2013 BDD equivalent to Figure 43 <\/td>\n<\/tr>\n
230<\/td>\n12.2.2 Local interactions
Figure 45 \u2013 Symbol for external elements <\/td>\n<\/tr>\n
231<\/td>\n12.2.3 Systemic dynamic interactions
12.2.4 Graphical representations of dynamic interactions <\/td>\n<\/tr>\n
232<\/td>\nFigure 46 \u2013 Dynamic interaction between a CCF and RBDs’ blocks
Figure 47 \u2013 Various ways to indicate dynamic interaction between blocks
Figure 48 \u2013 Dynamic interaction between a single repair team and RBDs’ blocks <\/td>\n<\/tr>\n
233<\/td>\nFigure 49 \u2013 Implementation of a PAND gate
Figure 50 \u2013 Equivalent finite-state automaton and exampleof chronogram for a PAND gate
Figure 51 \u2013 Implementation of a SEQ gate <\/td>\n<\/tr>\n
234<\/td>\n12.2.5 Probabilistic calculations
Figure 52 \u2013 Equivalent finite-state automaton and exampleof chronogram for a SEQ gate <\/td>\n<\/tr>\n
235<\/td>\nAnnexes
Annex A (informative) Summary of formulae
Table A.1 \u2013 Example of equations for calculating the probability of success of basic configurations <\/td>\n<\/tr>\n
239<\/td>\nAnnex B (informative) Boolean algebra methods
B.1 Introductory remarks
B.2 Notation <\/td>\n<\/tr>\n
240<\/td>\nB.3 Tie sets (success paths) and cut sets (failure paths) analysis
B.3.1 Notion of cut and tie sets
Figure B.1 \u2013 Examples of minimal tie sets (success paths)
Figure B.2 \u2013 Examples of non-minimal tie sets (non minimal success paths) <\/td>\n<\/tr>\n
241<\/td>\nB.3.2 Series-parallel representation using minimal tie and cut sets
Figure B.3 \u2013 Examples of minimal cut sets
Figure B.4 \u2013 Examples of non-minimal cut sets <\/td>\n<\/tr>\n
242<\/td>\nB.3.3 Identification of minimal cuts and tie sets
Figure B.5 \u2013 Example of RBD with tie and cut sets of various order <\/td>\n<\/tr>\n
243<\/td>\nB.4 Principles of calculations
B.4.1 Series structures
B.4.2 Parallel structures <\/td>\n<\/tr>\n
245<\/td>\nB.4.3 Mix of series and parallel structures
B.4.4 m out of n architectures (identical items) <\/td>\n<\/tr>\n
246<\/td>\nB.5 Use of Sylvester-Poincar\u00e9 formula for large RBDs and repeated blocks
B.5.1 General
B.5.2 Sylvester-Poincar\u00e9 formula with tie sets <\/td>\n<\/tr>\n
248<\/td>\nB.5.3 Sylvester-Poincar\u00e9 formula with cut sets <\/td>\n<\/tr>\n
249<\/td>\nB.6 Method for disjointing Boolean expressions
B.6.1 General and background <\/td>\n<\/tr>\n
250<\/td>\nB.6.2 Disjointing principle <\/td>\n<\/tr>\n
251<\/td>\nB.6.3 Disjointing procedure
B.6.4 Example of application of disjointing procedure <\/td>\n<\/tr>\n
253<\/td>\nB.6.5 Comments <\/td>\n<\/tr>\n
254<\/td>\nB.7 Binary decision diagrams
B.7.1 Establishing a BDD
Figure B.6 \u2013 Reminder of the RBD in Figure 35
Figure B.7 \u2013 Shannon decomposition of the Boolean function represented by Figure B.6 <\/td>\n<\/tr>\n
255<\/td>\nFigure B.8 \u2013 Identification of the parts which do not matter
Figure B.9 \u2013 Simplification of the Shannon decomposition <\/td>\n<\/tr>\n
256<\/td>\nB.7.2 Minimal success paths and cut sets with BDDs
Figure B.10 \u2013 Binary decision diagram related to the RBD in Figure B.6
Figure B.11 \u2013 Obtaining success paths (tie sets) from an RBD <\/td>\n<\/tr>\n
257<\/td>\nFigure B.12 \u2013 Obtaining failure paths (cut sets) from an RBD
Figure B.13 \u2013 Finding cut and tie sets from BDDs <\/td>\n<\/tr>\n
258<\/td>\nB.7.3 Probabilistic calculations with BDDs
Figure B.14 \u2013 Probabilistic calculations from a BDD <\/td>\n<\/tr>\n
259<\/td>\nB.7.4 Key remarks about the use of BDDs
Figure B.15 \u2013 Calculation of conditional probabilities using BDDs <\/td>\n<\/tr>\n
260<\/td>\nAnnex 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 \u2013 Principle of time dependent availability calculations <\/td>\n<\/tr>\n
261<\/td>\nC.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 <\/td>\n<\/tr>\n
263<\/td>\nC.4 RBD driven Markov processes
Figure C.2 \u2013 Principle of RBD driven Markov processes
Figure C.3 \u2013 Typical availability of RBD with quickly repaired failures <\/td>\n<\/tr>\n
264<\/td>\nC.5 Average and asymptotic (steady state) availability calculations
Figure C.4 \u2013 Example of simple multi-phase Markov process
Figure C.5 \u2013 Typical availability of RBD with periodically tested failures <\/td>\n<\/tr>\n
265<\/td>\nC.6 Frequency calculations <\/td>\n<\/tr>\n
266<\/td>\nC.7 Reliability calculations <\/td>\n<\/tr>\n
268<\/td>\nAnnex D (informative) Importance factors
D.1 General
D.2 Vesely-Fussell importance factor
D.3 Birnbaum importance factor or marginal importance factor <\/td>\n<\/tr>\n
269<\/td>\nD.4 Lambert importance factor or critical importance factor
D.5 Diagnostic importance factor <\/td>\n<\/tr>\n
270<\/td>\nD.6 Risk achievement worth
D.7 Risk reduction worth
D.8 Differential importance measure <\/td>\n<\/tr>\n
271<\/td>\nD.9 Remarks about importance factors <\/td>\n<\/tr>\n
272<\/td>\nAnnex 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 \u2013 Example of a sub-PN modelling a DRBD block <\/td>\n<\/tr>\n
273<\/td>\nFigure E.2 \u2013 Example of a sub-PN modelling a common cause failure
Figure E.3 \u2013 Example of DRBD based on RBD driven PN <\/td>\n<\/tr>\n
274<\/td>\nE.3 Evaluation of the DRBD state
Figure E.4 \u2013 Logical calculation of classical RBD structures
Figure E.5 \u2013 Example of logical calculation for an n\/m gate <\/td>\n<\/tr>\n
275<\/td>\nFigure E.6 \u2013 Example of sub-PN modelling a PAND gate with 2 inputs <\/td>\n<\/tr>\n
276<\/td>\nE.4 Availability, reliability, frequency and MTTF calculations
Figure E.7 \u2013 Example of the inhibition of the failure of a block
Figure E.8 \u2013 Sub-PN for availability, reliability and frequency calculations <\/td>\n<\/tr>\n
277<\/td>\nAnnex F (informative) Numerical examples and curves
F.1 General
F.2 Typical series RBD structure
F.2.1 Non-repaired blocks
Figure F.1 \u2013 Availability\/reliability of a typical non-repaired series structure <\/td>\n<\/tr>\n
278<\/td>\nF.2.2 Repaired blocks
Figure F.2 \u2013 Failure rate and failure frequency related to Figure F.1
Figure F.3 \u2013 Equivalence of a non-repaired series structure to a single block
Figure F.4 \u2013 Availability\/reliability of a typical repaired series structure <\/td>\n<\/tr>\n
279<\/td>\nF.3 Typical parallel RBD structure
F.3.1 Non-repaired blocks
Figure F.5 \u2013 Failure rate and failure frequency related to Figure F.4
Figure F.6 \u2013 Availability\/reliability of a typical non-repaired parallel structure <\/td>\n<\/tr>\n
280<\/td>\nF.3.2 Repaired blocks
Figure F.7 \u2013 Failure rate and failure frequency related to Figure F.6
Figure F.8 \u2013 Availability\/reliability of a typical repaired parallel structure <\/td>\n<\/tr>\n
281<\/td>\nF.4 Complex RBD structures
F.4.1 Non series-parallel RBD structure
Figure F.9 \u2013 Vesely failure rate and failure frequency related to Figure F.8
Figure F.10 \u2013 Example 1 from 7.5.2 <\/td>\n<\/tr>\n
282<\/td>\nF.4.2 Convergence to asymptotic values versus MTTR
Figure F.11 \u2013 Failure rate and failure frequency related to Figure F.10 <\/td>\n<\/tr>\n
283<\/td>\nF.4.3 System with periodically tested components
Figure F.12 \u2013 Impact of the MTTR on the convergence quickness <\/td>\n<\/tr>\n
284<\/td>\nFigure F.13 \u2013 System with periodically tested blocks
Figure F.14 \u2013 Failure rate and failure frequency related to Figure F.13 <\/td>\n<\/tr>\n
285<\/td>\nF.5 Dynamic RBD example
F.5.1 Comparison between analytical and Monte Carlo simulation results
F.5.2 Dynamic RBD example
Figure F.15 \u2013 Analytical versus Monte Carlo simulation results <\/td>\n<\/tr>\n
286<\/td>\nFigure F.16 \u2013 Impact of CCF and limited number of repair teams
Table F.1 \u2013 Impact of functional dependencies <\/td>\n<\/tr>\n
287<\/td>\nFigure F.17 \u2013 Markov graphs modelling the impact of the number of repair teams
Figure F.18 \u2013 Approximation for two redundant blocks <\/td>\n<\/tr>\n
288<\/td>\nBibliography <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Tracked Changes. Reliability block diagrams<\/b><\/p>\n\n\n\n\n
Published By<\/td>\nPublication Date<\/td>\nNumber of Pages<\/td>\n<\/tr>\n
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