Systems Dependability Assessment: Benefits of Petri Net Models

Petri Nets were defined for the study of discrete events systems and later extended for many purposes including dependability assessment. In our knowledge, no book deals specifically with the use of different type of PN to dependability. We propose in addition to bring a focus on the adequacy of Petri net types to the study of various problems related to dependability such as risk analysis and probabilistic assessment. In the first part, the basic models of PN and some useful extensions are briefly recalled. In the second part, the PN are used as a formal model to describe the evolution process of critical system in the frame of an ontological approach. The third part focuses on the stochastic Petri Nets (SPN) and their use in dependability assessment. Different formal models of SPN are formally presented (semantics, evolution rules…) and their equivalence with the corresponding class of Markov processes to get an analytical assessment of dependability. Simplification methods are proposed in order to reduce the size of analytical model and to make it more calculable. The introduction of some concepts specific to high level PN allows too the consideration of complex systems. Few applications in the field of the instrumentation and control (l&C) systems, safety integrated systems (SIS) emphasize the benefits of SPN for dependability assessment.

Table of Contents:
Introduction xi Part 1 Short Review of Petri Net Modeling 1 Introduction to Part 1 3 Chapter 1 Autonomous Petri Nets 5 1.1 Unmarked Petri nets 5 1.1.1 Definitions 5 1.1.2 Drawing 6 1.1.3 Other definitions 7 1.2 Marking of a PN 7 1.2.1 Order relation on markings 8 1.2.2 Enabled transition 9 1.3 Dynamics of autonomous PNs 9 1.3.1 Firing of a transition 9 1.3.2 Transition matrix 11 1.3.3 Firing sequence 11 1.3.4 Reachable marking 12 1.3.5 Fundamental equation 12 1.3.6 Properties of PN 14 1.3.7 Other properties 14 1.3.8 Invariants in a PN 15 1.3.9 Reachability graph 16 Chapter 2 Petri Nets and Event Languages 19 2.1 Labeled PNs 19 2.1.1 Formal definition 19 2.1.2 Generated and marked languages 20 2.2 Example 21 Chapter 3 Comparison Petri Nets – Finite State Automaton 25 3.1 Language expression 26 3.2 Building of the models 27 3.2.1 Synchronization of submodels 28 3.2.2 Resource sharing 29 3.2.3 Construction by refinement 30 3.3 Compactness of the model 32 Chapter 4 Some Extensions of Petri Nets 35 4.1 PN with inhibitor arcs 35 4.2 Timed PN 36 4.2.1 P-timed Petri nets 37 4.2.2 T-timed Petri nets 37 4.3 Synchronized PN 38 4.4 Timed synchronized PN 40 4.5 Interpreted PN 41 4.6 Colored PN 42 4.6.1 Introduction example 42 4.6.2 Formal definition 45 4.6.3 A dedicated software CPN Tools 46 Conclusion to Part 1 51 Part 2 A Formal Approach to Risk Assessment 53 Introduction to Part 2 51 Chapter 5 Ontology-based Accidental Process 61 5.1 Preliminary definitions 61 5.2 Elementary entities: HSE and VTE 63 5.2.1 Hazard supplier entity (HSE) 63 5.2.2 Vulnerable target entity (VTE) 63 5.3 Elementary situations and elementary events 64 5.3.1 State versus situation 64 5.3.2 Initial situation (IS) 64 5.3.3 Initiating event (IEv) 64 5.3.4 Hazard situation (HS) 65 5.3.5 Exposure event (EEv) 65 5.3.6 Exposure situation (ES) 65 5.3.7 Accident situation 65 5.3.8 Hazardous (feared) event (HEv) 65 5.4 Conclusion 66 Chapter 6 Petri Net Modeling of the Accidental Process 67 6.1 Elementary process 68 6.2 Sequence of elementary processes 71 6.3 Modeling the action of a safety barrier 71 6.4 Modeling of a cumulative process 73 6.5 PN as a support for risk assessment 75 6.5.1 Modeling of the damage 75 6.5.2 Modeling of the event frequencies 75 6.5.3 CPN Tools implementation 77 6.5.4 Evaluation rule of the risk 83 6.6 Conclusion 86 Chapter 7 Illustrative Example 87 7.1 Functional description 87 7.2 Building of an accidental process 88 7.2.1 First elementary process 88 7.2.2 Second elementary process 91 7.2.3 Parallel process 92 7.2.4 The whole model 92 7.3 Conclusion 94 Chapter 8 Design and Safety Assessment Cycle 95 8.1 Five essential steps 95 8.2 Ontological interest 98 Conclusion to Part 2 101 Part 3 Stochastic Petri Nets 103 Introduction to Part 3 105 Chapter 9 Basic Concept 107 9.1 Introductory example 107 9.2 Formal definition 108 Chapter 10 Semantics, Properties and Evolution Rules of an SPN 111 10.1 Conservatism properties 112 10.1.1 Conservatism of the mean marking in steady state 112 10.1.2 Conservatism of the flow in steady state 113 10.2 Mean sojourn time in a place of a SPN 113 10.3 Equivalent Markov process 114 10.4 Example of SPN for systems dependability modelling and assessment 116 Chapter 11 Simplification of Complex Models 121 11.1 Introduction 121 11.2 System modeling 122 11.3 Presentation of the quantitative analysis method 124 11.3.1 Steps to obtain an aggregated Markov graph 124 11.3.2 Toward a direct establishment of a reduced Markov graph 137 11.4 Example 137 11.4.1 Failure modeling 138 11.4.2 Study of the different functional and hardware solutions 139 11.4.3 Evaluation of the weighting coefficients from the Petri nets 144 11.4.4 Conclusion 147 Chapter 12 Extensions of SPN 149 12.1 Introduction 149 12.2 Relationship between stochastic Petri nets and stochastic processes 150 12.3 The transition firing policy 151 12.4 Associated stochastic processes 151 12.4.1 Temporal memory based on resampling 152 12.4.2 Temporal memory based on age memory or on enabling memory 153 12.4.3 Stochastic process underlying a stochastic PN 154 12.4.4 Embedded Markov chain of the stochastic process 157 12.4.5 Application to a case study 159 12.5 Synchronization problem in generalized stochastic Petri nets 162 12.5.1 GSPN with internal synchronization 162 12.5.2 SPN with predicates and assertions 164 12.6 Conclusion 168 Part 4 Applications of Stochastic Petri Nets to Assessment Problems in Industrial Systems 169 Introduction to Part 4 171 Chapter 13 Application in Dynamic Reliability 175 13.1 Presentation of the system and hypothesis 175 13.2 System modeling with Petri net 177 13.3 Methodology application 179 13.4 Construction of an aggregated Markov graph 180 13.5 Conclusion 185 Chapter 14 Classical Dependability Assessment 187 14.1 Availability study of a nuclear power plant subsystem 187 14.1.1 CPN modeling 188 14.1.2 Reliability and dependability assessment 192 14.1.3 Conclusion 196 14.2 Common causes failures in nuclear plants (safety oriented) 197 14.2.1 The Atwood model 197 14.2.2 Case study 199 14.2.3 Probabilistic dependability assessment 208 14.2.4 Conclusion 212 Chapter 15 Impact of Failures on System Performances 213 15.1 Reliability evaluation of networked control system 213 15.1.1 Statement of the problem 213 15.1.2 Reliability criteria of an NCS 215 15.1.3 Elements of modeling 216 15.1.4 Simulation and results 225 15.1.5 Evaluation of reliability 230 15.1.6 Conclusion 230 15.2 Railway signaling 231 15.2.1 Introduction 231 15.2.2 Interest 233 15.2.3 Signaling system specifications 234 15.2.4 Elements to be modeled 235 15.2.5 Architecture of the model 236 15.2.6 Example of an elementary model 237 15.2.7 Incident generation 239 15.2.8 Results 239 15.2.9 Conclusion 242 Conclusion 245 Appendix 247 Bibliography 251 Index 261