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BS EN 62551:2012

BS EN 62551:2012

$198.66

Analysis techniques for dependability. Petri net techniques

Published By Publication Date Number of Pages
BSI 2012 67
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IEC 62551:2012 provides guidance on a Petri net based methodology for dependability purposes. It supports modelling a system, analysing the model and presenting the analysis results. This methodology is oriented to dependability-related measures with all the related features, such as reliability, availability, production availability, maintainability and safety (e.g. safety integrity level (SIL) [2] related measures). Key words: Petri net based methodology for dependability purposes

PDF Catalog

PDF Pages PDF Title
6 English
CONTENTS
9 INTRODUCTION
10 1 Scope
2 Normative references
3 Terms, definitions, symbols and abbreviations
3.1 Terms and definitions
12 3.2 Symbols and abbreviations
Tables
Table 1 – Symbols in untimed Petri nets
13 Table 2 – Additional symbols in timed Petri nets
Table 3 – Symbols for hierarchical modelling
14 4 General description of Petri nets
4.1 Untimed low-level Petri nets
4.2 Timed low-level Petri nets
15 4.3 High-level Petri nets
4.4 Extensions of Petri nets and modelling with Petri nets
4.4.1 Further representations of Petri net elements
Figures
Figure 1 – Weighted inhibitor arc
16 4.4.2 Relationship to the concepts of dependability
Figure 2 – Place p is a multiple place
Figure 3 – Marking on p after firing of transition t
Figure 4 – The activation of t depends on the value of V
17 5 Petri net dependability modelling and analysis
5.1 The steps to be performed in general
Figure 5 – Methodology consisting mainly of ‘modelling’, ‘analysing’ and ‘representing’ steps
Figure 6 – Process for dependability modelling and analysing with Petri nets
Table 4 – Corresponding concepts in systems, Petri nets and dependability
18 5.2 Steps to be performed in detail
5.2.1 General
5.2.2 Description of main parts and functions of the system (Step 1)
5.2.3 Modelling the structure of the system on the basis of Petri net-submodels and their relations (Step 2)
19 Figure 7 – Modelling structure concerning the two main parts ‘plant’ and ‘control’ with models for their functions and dependability
20 5.2.4 Refining the models of Step 2 until the required level of detail is achieved (Step 3)
5.2.5 Analysing the model to achieve the results of interest (Step 4)
21 5.2.6 Representation and interpretation of results of analyses (Step 5)
Figure 8 – Indication of the analysis method as a function of the PN model
22 5.2.7 Summary of documentation (Step 6)
6 Relationship to other dependability models
Table 5 – Mandatory and recommended parts of documentation
24 Annex A (informative) Structure and dynamics of Petri nets
Figure A.1 – Availability state-transition circle of a component
25 Figure A.2 – Transition ‘failure’ is enabled
Figure A.3 – ‘Faulty’ place marked due to firing of ‘failure’
26 Figure A.4 – Transition ‘comp1 repair’ is enabled
Figure A.5 – The token at the ‘maintenance crew available’ location is not used
27 Figure A.6 – Transition is not enabled
Figure A.7 – Marking before firing
Figure A.8 – Marking after firing
Figure A.9 – PN with initial marking
Figure A.10 – Corresponding RG
28 Figure A.11 – Transitions ‘complp repair’ and ‘comphp failure’ are enabled
Table A.1 – Corresponding concepts in systems, Petri nets,reachability graphs and dependability
29 Figure A.12 – Marking after firing of transition ‘complp repair’
30 Figure A.13 – A timed PN with two exponentially distributed timed transitions
Figure A.14 – The corresponding stochastic reachability graph
31 Figure A.15 – Petri net with timed transitions
34 Table A.2 – Place and transition with rewards
35 Annex B (informative) Availability with redundancy m-out-of-n
Figure B.1 – Two individual item availabilitynets with specific failure- and repair-rates
Figure B.2 – Stochastic reachability graph corresponding to Figure B.1 with global states (as an abbreviation c1 is used for “comp1 faulty”)
Figure B.3 – Three individual item availability nets with specific failure rates and repair rates
36 Figure B.4 – Stochastic reachability graph corresponding to Figure B.3 with global states (as an abbreviation c1 is used for ‘comp1 faulty’)
37 Figure B.5 – Specifically connected 1-out-of-3 availability net
Figure B.6 – Specifically connected 2-out-of-3 availability net
38 Figure B.7 – Specifically connected 3-out-of-3 availability net
Figure B.8 – Stochastic reachability graph with system specific operating states
39 Figure B.9 – Specifically connected 1-out-of-3 reliability net
Figure B.10 – Reachability graph for the net in Figure B.9
Figure B.11 – Specifically connected 2-out-of-3 reliability net
Figure B.12 – Reachability graph for the net in Figure B.11
40 Figure B.13 – Specifically connected 3-out-of-3 reliability net
Figure B.14 – Reachability graph for the net in Figure B.13
41 Annex C (informative) Abstract example
Figure C.1 – Individual availability net
Figure C.2 – Stochastic availability graph of the net in Figure C.1 with its global states and aggregated global states according to availability and safety
42 Figure C.3 – Basic reliability and function modelling concept
43 Figure C.4 – General hierarchical net with supertransitions to model reliability
Figure C.5 – General hierarchical net with supertransitions and superplaces
Figure C.6 – General hierarchical net with supertransitions to model availability
44 Figure C.7 – General hierarchical net with supertransitions and superplaces
45 Annex D (informative) Modelling typical dependability concepts
Table D.1 – Dependability concepts modelled with PN structures
46 Table D.2 – Modelling costs of states and events
47 Annex E (informative) Level-crossing example
Figure E.1 – Applied example of a level crossing and its protection system
48 Figure E.2 – Main parts of the level crossing example model
49 Figure E.3 – Submodels of the level crossing example model
50 Figure E.4 – PN model of car and train traffic processes
51 Figure E.5 – PN model of the traffic processes and traffic dependability
52 Figure E.6 – PN model of the traffic process with an ideal control function
53 Figure E.7 – PN model of the level crossing example model
54 Figure E.8 – Collected measures of the road traffic flow of a particular level crossing: Time intervals between two cars coming to the level crossing
Table E.1 – Car-related places in the submodel ‘Traffic process’ (see Figure E.4)
55 Figure E.9 – Approximated probability distribution function based on the measures depicted in Figure E.5
Figure E.10 – Collected measurements of time spent by road vehicle in the danger zone of the level crossing
56 Figure E.11 – Approximated probability distribution function based on measurements depicted in Figure E.10
57 Table E.2 – Car-traffic related transitions in the submodel ‘Traffic process’ and Traffic dependability (see Figure E.7)
Table E.3 – Train-traffic related places in the submodel ‘Traffic process’(see Figure E.7)
58 Table E.4 – Train-traffic related transitions in the submodel ‘Traffic process’ (see Figure E.7)
Table E.5 – Places in the submodel ‘Traffic dependability’ (see Figure E.7)
Table E.6 – Transitions in the submodel ‘Traffic dependability’ (see Figure E.7)
59 Table E.7 – Places in the submodel ‘Control function’ (see Figure E.7)
Table E.8 – Transitions in the submodel ‘Control function’ (see Figure E.7)
Table E.9 – Places in the submodel ‘Control equipment dependability’ (see Figure E.7)
60 Table E.10 – Transitions in the submodel ‘Control equipment dependability’ (see Figure E.7)
61 Figure E.12 – Aggregated RG and information about the corresponding states
Table E.11 – Specification of boolean conditions for states to be subsumedin an aggregated state
62 Figure E.13 – Results of the quantitative analysis showing the level crossing average availability for road traffic users as a function of the protection equipment hazard rate for different used activation and approaching times TAC
Figure E.14 – Results of the quantitative analysis showing the individual risk of the level crossing users as a function of the protection equipment hazard rate for different used activation and approaching times TAC
63 Figure E.15 – Availability safety diagram based on the quantitative results of the model analysis shown in Figure E.13 and Figure E.14
64 Bibliography

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BS EN 62551:2012
$198.66