Systems Dependability Assessment E-Book

Jean-Francois Aubry

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 309

Veröffentlichungsjahr: 2016

Beschreibung

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.

Leseprobe

Table of Contents

Cover

Title

Copyright

Introduction

PART 1: Short Review of Petri Net Modeling

Introduction to Part 1

1 Autonomous Petri Nets

1.1. Unmarked Petri nets

1.2. Marking of a PN

1.3. Dynamics of autonomous PNs

2 Petri Nets and Event Languages

2.1. Labeled PNs

2.2. Example

3 Comparison Petri Nets – Finite State Automaton

3.1. Language expression

3.2. Building of the models

3.3. Compactness of the model

4 Some Extensions of Petri Nets

4.1. PN with inhibitor arcs

4.2. Timed PN

4.3. Synchronized PN

4.4. Timed synchronized PN

4.5. Interpreted PN

4.6. Colored PN

Conclusion to Part 1

PART 2: A Formal Approach to Risk Assessment

Introduction to Part 2

5 Ontology-based Accidental Process

5.1. Preliminary definitions

5.2. Elementary entities: HSE and VTE

5.3. Elementary situations and elementary events

5.4. Conclusion

6 Petri Net Modeling of the Accidental Process

6.1. Elementary process

6.2. Sequence of elementary processes

6.3. Modeling the action of a safety barrier

6.4. Modeling of a cumulative process

6.5. PN as a support for risk assessment

6.6. Conclusion

7 Illustrative Example

7.1. Functional description

7.2. Building of an accidental process

7.3. Conclusion

8 Design and Safety Assessment Cycle

8.1. Five essential steps

8.2. Ontological interest

Conclusion to Part 2

PART 3: Stochastic Petri Nets

Introduction to Part 3

9 Basic Concept

9.1. Introductory example

9.2. Formal definition

10 Semantics, Properties and Evolution Rules of an SPN

10.1. Conservatism properties

10.2. Mean sojourn time in a place of a SPN

10.3. Equivalent Markov process

10.4. Example of SPN for systems dependability modeling and assessment

11 Simplification of Complex Models

11.1. Introduction

11.2. System modeling

11.3. Presentation of the quantitative analysis method

11.4. Example

12 Extensions of SPN

12.1. Introduction

12.2. Relationship between stochastic Petri nets and stochastic processes

12.3. The transition firing policy

12.4. Associated stochastic processes

12.5. Synchronization problem in generalized stochastic Petri nets

12.6. Conclusion

PART 4: Applications of Stochastic Petri Nets to Assessment Problems in Industrial Systems

Introduction to Part 4

13 Application in Dynamic Reliability

13.1. Presentation of the system and hypothesis

13.2. System modeling with Petri net

13.3. Methodology application

13.4. Construction of an aggregated Markov graph

13.5. Conclusion

14 Classical Dependability Assessment

14.1. Availability study of a nuclear power plant subsystem

14.2. Common causes failures in nuclear plants (safety oriented)

15 Impact of Failures on System Performances

15.1. Reliability evaluation of networked control system

15.2. Railway signaling

Conclusion

Appendix

A.1. Complements on Petri nets basics

Bibliography

Index

End User License Agreement

List of Tables

6 Petri Net Modeling of the Accidental Process

Table 6.1.

Simulation results of accidental process

13 Application in Dynamic Reliability

Table 13.1.

Control of actuators

Table 13.2.

Description of the places

Table 13.3.

Description of the messages

14 Classical Dependability Assessment

Table 14.1.

Components MTTF and MTTR, (in hour)

Table 14.2.

System performance results

Table 14.3.

The values of occurrence frequencies

μ

and

ω

for non-lethal and lethal shocks as a function of p

Table 14.4.

Real and visible PFD of the protection I&C system for different values of

p

Table 14.5.

Combinations of failed boards leading to the system downtime depending on p

1

and p

2

15 Impact of Failures on System Performances

Table 15.1.

Probability of failure by stability

List of Illustrations

1 Autonomous Petri Nets

Figure 1.1.

The drawing of a PN

Figure 1.2.

A marked PN

Figure 1.3.

PN of Figure 1.2 after firing of transition T

2

Figure 1.4.

PN state of Figure 1.3 after firing of transition

T

1

Figure 1.5.

A marked PN and its reachability graph

2 Petri Nets and Event Languages

Figure 2.1.

PN of an assembly system

3 Comparison Petri Nets – Finite State Automaton

Figure 3.1.

Arborescent automaton equivalent to the language a

n

b

n

Figure 3.2.

Labeled PN equivalent to the language a

n

b

n

Figure 3.3.

Simple case of two PNs synchronization

Figure 3.4.

Resource sharing between two sub-PNs

Figure 3.5.

The three construction primitives

Figure 3.6.

Application example of the primitives

4 Some Extensions of Petri Nets

Figure 4.1.

PN with inhibitor arc

Figure 4.2.

Synchronization mechanism

Figure 4.3.

Introductive example of colored PN

Figure 4.4.

An example of CPN Tools model

Figure 4.5.

Hierarchy in CPN Tools

6 Petri Net Modeling of the Accidental Process

Figure 6.1.

Synchronized PN of an elementary accidental process

Figure 6.2.

Completed elementary accidental process

Figure 6.3.

Chain of elementary processes

Figure 6.4.

Action model of a protection barrier

Figure 6.5.

Modeling of the cumulative process

Figure 6.6.

PN model of the event generator (mean values)

Figure 6.7.

Event generator CPN Tools model (stochastic values)

Figure 6.8.

Simulation model of a sequence of two elementary processes

Figure 6.9.

Simulation model of the elementary process

7 Illustrative Example

Figure 7.1.

The system train – screen doors

Figure 7.2.

Elementary process: “passenger hurt by untimely door closing”

Figure 7.3.

Elementary process “untimely door closing”

Figure 7.4.

The whole accidental process

8 Design and Safety Assessment Cycle

Figure 8.1.

Design and Safety Assessment Cycle

9 Basic Concept

Figure 9.1.

Stochastic Petri net of the machining system with two machines

10 Semantics, Properties and Evolution Rules of an SPN

Figure 10.1.

The hydraulic system

Figure 10.2.

PN of the hydraulic system

Figure 10.3.

PN with repairer sharing

Figure 10.4.

The reachability graph homogeneous to a Markov graph

11 Simplification of Complex Models

Figure 11.1.

Example of a control system modeling and its failures

Figure 11.2.

Example of reachability graph

Figure 11.3.

Modeling into a Markov process

Figure 11.4.

Aggregated Markov graph

Figure 11.5.

Failure modeling and interaction with the control

Figure 11.6.

PN model of the control system

Figure 11.7.

“Stochastization” of the control transitions

Figure 11.8.

Markov graph of the fourth model

Figure 11.9.

Aggregated Markov graph

Figure 11.10.

Two examples of sub-PNs

12 Extensions of SPN

Figure 12.1.

Underlying PN of the model

Figure 12.2.

Emission of a signal X

i

by P

i

and receipt of X

i

by T

j

Figure 12.3.

PN representation of the first entity

Figure 12.4.

PN representation of the repairmen

13 Application in Dynamic Reliability

Figure 13.1.

The “tank-valve-pumps” system

Figure 13.2.

Modeling of the system in Petri nets

Figure 13.3.

The aggregated Markov graph of the system

Figure 13.4.

Probabilitly evolution of the feared event ER

14 Classical Dependability Assessment

Figure 14.1.

Reliability block diagram of the TPAs system

Figure 14.2.

Concurrence of GSPN stochastic transitions

Figure 14.3.

GSPN modeling behavior with a timed CPN

Figure 14.4.

CPN models associated with the case study

Figure 14.5.

Empirical distribution of the MTTFF, MTBF and MMTR of the whole controlled system

Figure 14.6.

Architecture of the case study I&C system for a nuclear power plant

Figure 14.7.

High level colored Petri net of the I&C system

Figure 14.8.

CPN subnet modeling the non-lethal CCF

Figure 14.9.

CPN subnet modeling the lethal CCF

Figure 14.10.

CPN sub-net of an electronic board

Figure 14.11.

CPN sub-net to determine the state of the whole I&C system (available or unavailable)

15 Impact of Failures on System Performances

Figure 15.1.

Structure of an NCS

Figure 15.2.

System-level CPN model

Figure 15.3.

Process CPN model

Figure 15.4.

Sensor CPN model

Figure 15.5.

Controller CPN model

Figure 15.6.

Actuator CPN model

Figure 15.7.

Network CPN model

Figure 15.8.

Probability of failure by overshoot in the presence of variable delays, the x-axis represents the constraint of the D

ov

threshold (expressed in % of the setpoint), the y-axis represents the value of the probability of failure

Figure 15.9.

Probability of failure by overshoot in the presence of losses of information, the x-axis represents the constraint of the D

ov

threshold (expressed in % of the setpoint), the y-axis represents the value of the probability of failure

Figure 15.10.

Probability of failure by overshoot in the presence of the losses and the variable delays, the x-axis represents the constraint of the D

ov

threshold (expressed in % of the setpoint), the y-axis represents the value of the probability of failure

Figure 15.11.

Trend to instability

Figure 15.12.

MA assignment as a function of the lateral signaling

Figure 15.13.

Example of CTPN, transmission of the BAL signaling

Figure 15.14.

Example of token statement

Figure 15.15.

Comparison of real and simulated schedules on the Zoufftgen-Woippy rail network

Figure 15.16.

Comparison ETCS/BAL in case of failure of a track circuit

Figure 15.17.

Comparison ETCS/BAL in case of breaking of the train coupling

Appendix

Figure A.1.

State graph

Figure A.2.

Event graph

Figure A.3.

Lock and trap in a PN

Guide

Cover

Table of Contents

Begin Reading

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Systems Dependability Assessment

Benefits of Petri Net Models

Jean-François Aubry

Nicolae Brinzei

Mohammed-Habib Mazouni

Systems Dependability Assessment Set

coordinated by

Jean-François Aubry