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<\/p>\n
| PDF Pages<\/th>\n | PDF Title<\/th>\n<\/tr>\n | ||||||
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| 6<\/td>\n | English CONTENTS <\/td>\n<\/tr>\n | ||||||
| 9<\/td>\n | INTRODUCTION <\/td>\n<\/tr>\n | ||||||
| 10<\/td>\n | 1 Scope 2 Normative references 3 Terms, definitions, symbols and abbreviations 3.1 Terms and definitions <\/td>\n<\/tr>\n | ||||||
| 12<\/td>\n | 3.2 Symbols and abbreviations Tables Table 1 \u2013 Symbols in untimed Petri nets <\/td>\n<\/tr>\n | ||||||
| 13<\/td>\n | Table 2 \u2013 Additional symbols in timed Petri nets Table 3 \u2013 Symbols for hierarchical modelling <\/td>\n<\/tr>\n | ||||||
| 14<\/td>\n | 4 General description of Petri nets 4.1 Untimed low-level Petri nets 4.2 Timed low-level Petri nets <\/td>\n<\/tr>\n | ||||||
| 15<\/td>\n | 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 \u2013 Weighted inhibitor arc <\/td>\n<\/tr>\n | ||||||
| 16<\/td>\n | 4.4.2 Relationship to the concepts of dependability Figure 2 \u2013 Place p is a multiple place Figure 3 \u2013 Marking on p after firing of transition t Figure 4 \u2013 The activation of t depends on the value of V <\/td>\n<\/tr>\n | ||||||
| 17<\/td>\n | 5 Petri net dependability modelling and analysis 5.1 The steps to be performed in general Figure 5 \u2013 Methodology consisting mainly of \u2018modelling\u2019, \u2018analysing\u2019 and \u2018representing\u2019 steps Figure 6 \u2013 Process for dependability modelling and analysing with Petri nets Table 4 \u2013 Corresponding concepts in systems, Petri nets and dependability <\/td>\n<\/tr>\n | ||||||
| 18<\/td>\n | 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) <\/td>\n<\/tr>\n | ||||||
| 19<\/td>\n | Figure 7 \u2013 Modelling structure concerning the two main parts ‘plant’ and ‘control’ with models for their functions and dependability <\/td>\n<\/tr>\n | ||||||
| 20<\/td>\n | 5.2.4 Refining the models of Step 2 until the required level of detail is achieved (Step\u00a03) 5.2.5 Analysing the model to achieve the results of interest (Step 4) <\/td>\n<\/tr>\n | ||||||
| 21<\/td>\n | 5.2.6 Representation and interpretation of results of analyses (Step 5) Figure 8 \u2013 Indication of the analysis method as a function of the PN model <\/td>\n<\/tr>\n | ||||||
| 22<\/td>\n | 5.2.7 Summary of documentation (Step 6) 6 Relationship to other dependability models Table 5 \u2013 Mandatory and recommended parts of documentation <\/td>\n<\/tr>\n | ||||||
| 24<\/td>\n | Annex A (informative) Structure and dynamics of Petri nets Figure A.1 \u2013 Availability state-transition circle of a component <\/td>\n<\/tr>\n | ||||||
| 25<\/td>\n | Figure A.2 \u2013 Transition \u2018failure\u2019 is enabled Figure A.3 \u2013 \u2018Faulty\u2019 place marked due to firing of \u2018failure’ <\/td>\n<\/tr>\n | ||||||
| 26<\/td>\n | Figure A.4 \u2013 Transition \u2018comp1 repair\u2019 is enabled Figure A.5 \u2013 The token at the \u2018maintenance crew available\u2019 location is not used <\/td>\n<\/tr>\n | ||||||
| 27<\/td>\n | Figure A.6 \u2013 Transition is not enabled Figure A.7 \u2013 Marking before firing Figure A.8 \u2013 Marking after firing Figure A.9 \u2013 PN with initial marking Figure A.10 \u2013 Corresponding RG <\/td>\n<\/tr>\n | ||||||
| 28<\/td>\n | Figure A.11 \u2013 Transitions \u2018complp repair\u2019 and \u2018comphp failure\u2019 are enabled Table A.1 \u2013 Corresponding concepts in systems, Petri nets,reachability graphs and dependability <\/td>\n<\/tr>\n | ||||||
| 29<\/td>\n | Figure A.12 \u2013 Marking after firing of transition \u2018complp repair\u2019 <\/td>\n<\/tr>\n | ||||||
| 30<\/td>\n | Figure A.13 \u2013 A timed PN with two exponentially distributed timed transitions Figure A.14 \u2013 The corresponding stochastic reachability graph <\/td>\n<\/tr>\n | ||||||
| 31<\/td>\n | Figure A.15 \u2013 Petri net with timed transitions <\/td>\n<\/tr>\n | ||||||
| 34<\/td>\n | Table A.2 \u2013 Place and transition with rewards <\/td>\n<\/tr>\n | ||||||
| 35<\/td>\n | Annex B (informative) Availability with redundancy m-out-of-n Figure B.1 \u2013 Two individual item availabilitynets with specific failure- and repair-rates Figure B.2 \u2013 Stochastic reachability graph corresponding to Figure B.1 with global states (as an abbreviation c1 is used for \u201ccomp1 faulty\u201d) Figure B.3 \u2013 Three individual item availability nets with specific failure rates and repair rates <\/td>\n<\/tr>\n | ||||||
| 36<\/td>\n | Figure B.4 \u2013 Stochastic reachability graph corresponding to Figure B.3 with global states (as an abbreviation c1 is used for \u2018comp1 faulty\u2019) <\/td>\n<\/tr>\n | ||||||
| 37<\/td>\n | Figure B.5 \u2013 Specifically connected 1-out-of-3 availability net Figure B.6 \u2013 Specifically connected 2-out-of-3 availability net <\/td>\n<\/tr>\n | ||||||
| 38<\/td>\n | Figure B.7 \u2013 Specifically connected 3-out-of-3 availability net Figure B.8 \u2013 Stochastic reachability graph with system specific operating states <\/td>\n<\/tr>\n | ||||||
| 39<\/td>\n | Figure B.9 \u2013 Specifically connected 1-out-of-3 reliability net Figure B.10 \u2013 Reachability graph for the net in Figure B.9 Figure B.11 \u2013 Specifically connected 2-out-of-3 reliability net Figure B.12 \u2013 Reachability graph for the net in Figure B.11 <\/td>\n<\/tr>\n | ||||||
| 40<\/td>\n | Figure B.13 \u2013 Specifically connected 3-out-of-3 reliability net Figure B.14 \u2013 Reachability graph for the net in Figure B.13 <\/td>\n<\/tr>\n | ||||||
| 41<\/td>\n | Annex C (informative) Abstract example Figure C.1 \u2013 Individual availability net Figure C.2 \u2013 Stochastic availability graph of the net in Figure C.1 with its global states and aggregated global states according to availability and safety <\/td>\n<\/tr>\n | ||||||
| 42<\/td>\n | Figure C.3 \u2013 Basic reliability and function modelling concept <\/td>\n<\/tr>\n | ||||||
| 43<\/td>\n | Figure C.4 \u2013 General hierarchical net with supertransitions to model reliability Figure C.5 \u2013 General hierarchical net with supertransitions and superplaces Figure C.6 \u2013 General hierarchical net with supertransitions to model availability <\/td>\n<\/tr>\n | ||||||
| 44<\/td>\n | Figure C.7 \u2013 General hierarchical net with supertransitions and superplaces <\/td>\n<\/tr>\n | ||||||
| 45<\/td>\n | Annex D (informative) Modelling typical dependability concepts Table D.1 \u2013 Dependability concepts modelled with PN structures <\/td>\n<\/tr>\n | ||||||
| 46<\/td>\n | Table D.2 \u2013 Modelling costs of states and events <\/td>\n<\/tr>\n | ||||||
| 47<\/td>\n | Annex E (informative) Level-crossing example Figure E.1 \u2013 Applied example of a level crossing and its protection system <\/td>\n<\/tr>\n | ||||||
| 48<\/td>\n | Figure E.2 \u2013 Main parts of the level crossing example model <\/td>\n<\/tr>\n | ||||||
| 49<\/td>\n | Figure E.3 \u2013 Submodels of the level crossing example model <\/td>\n<\/tr>\n | ||||||
| 50<\/td>\n | Figure E.4 \u2013 PN model of car and train traffic processes <\/td>\n<\/tr>\n | ||||||
| 51<\/td>\n | Figure E.5 \u2013 PN model of the traffic processes and traffic dependability <\/td>\n<\/tr>\n | ||||||
| 52<\/td>\n | Figure E.6 \u2013 PN model of the traffic process with an ideal control function <\/td>\n<\/tr>\n | ||||||
| 53<\/td>\n | Figure E.7 \u2013 PN model of the level crossing example model <\/td>\n<\/tr>\n | ||||||
| 54<\/td>\n | Figure E.8 \u2013 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 \u2013 Car-related places in the submodel \u2018Traffic process\u2019 (see Figure E.4) <\/td>\n<\/tr>\n | ||||||
| 55<\/td>\n | Figure E.9 \u2013 Approximated probability distribution function based on the measures depicted in Figure E.5 Figure E.10 \u2013 Collected measurements of time spent by road vehicle in the danger zone of the level crossing <\/td>\n<\/tr>\n | ||||||
| 56<\/td>\n | Figure E.11 \u2013 Approximated probability distribution function based on measurements depicted in Figure E.10 <\/td>\n<\/tr>\n | ||||||
| 57<\/td>\n | Table E.2 \u2013 Car-traffic related transitions in the submodel \u2018Traffic process\u2019 and Traffic dependability (see Figure\u00a0E.7) Table E.3 \u2013 Train-traffic related places in the submodel \u2018Traffic process\u2019(see Figure\u00a0E.7) <\/td>\n<\/tr>\n | ||||||
| 58<\/td>\n | Table E.4 \u2013 Train-traffic related transitions in the submodel \u2018Traffic process\u2019 (see Figure E.7) Table E.5 \u2013 Places in the submodel \u2018Traffic dependability\u2019 (see Figure E.7) Table E.6 \u2013 Transitions in the submodel \u2018Traffic dependability\u2019 (see Figure E.7) <\/td>\n<\/tr>\n | ||||||
| 59<\/td>\n | Table E.7 \u2013 Places in the submodel \u2018Control function\u2019 (see Figure E.7) Table E.8 \u2013 Transitions in the submodel \u2018Control function\u2019 (see Figure E.7) Table E.9 \u2013 Places in the submodel \u2018Control equipment dependability\u2019 (see Figure E.7) <\/td>\n<\/tr>\n | ||||||
| 60<\/td>\n | Table E.10 \u2013 Transitions in the submodel \u2018Control equipment dependability\u2019 (see Figure E.7) <\/td>\n<\/tr>\n | ||||||
| 61<\/td>\n | Figure E.12 \u2013 Aggregated RG and information about the corresponding states Table E.11 \u2013 Specification of boolean conditions for states to be subsumedin an aggregated state <\/td>\n<\/tr>\n | ||||||
| 62<\/td>\n | Figure E.13 \u2013 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 \u2013 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 <\/td>\n<\/tr>\n | ||||||
| 63<\/td>\n | Figure E.15 \u2013 Availability safety diagram based on the quantitative results of the model analysis shown in Figure E.13 and Figure E.14 <\/td>\n<\/tr>\n | ||||||
| 64<\/td>\n | Bibliography <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":" Analysis techniques for dependability. Petri net techniques<\/b><\/p>\n |