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1 Public PhD defense Finite Degradation Structures A Unified Framework of Combinatorial Models in Probabilistic Risk/Safety Assessment PhD candidate: Liu Yang Supervisor: Professor Antoine Rauzy Co-Supervisor: Associate Professor Cecilia Haskins

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Finite Degradation Structures

A Unified Framework of Combinatorial Models in Probabilistic Risk/Safety Assessment

PhD candidate: Liu Yang Supervisor: Professor Antoine Rauzy Co-Supervisor: Associate Professor Cecilia Haskins Public PhD defense

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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www.ntnu.no

Outline

PhD Defense – June 2nd 2020, NTNU

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Introduction

Background and motivation Overview of PhD work

Main contributions

Theoretical development Computer-based implementation Interesting applications

Conclusion

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Background and motivation

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❑ Reliability and safety analysis aims at evaluating whether the system is reliable or safe enough to operate. ❑ To evaluate the reliability and safety of a system, we need indicators:

  • Scenarios: in what situation the system may fail
  • Probabilities: how probable the system may fail

❑ To obtain the indicators, we need to design models:

  • Combinatorial models (Fault trees and related formalisms like HiP-HOPS [Papadopoulos 2011],

multistate system approaches [Levitin 2003, Zaitseva 2013], ...)

  • State/transition models (Markov chains, Petri nets, Guarded Transition Systems [Rauzy 2008], ...)

Introduction

  • Background and motivation
  • Overview of PhD work

Main contributions Conclusion

Papadopoulos, Y., Walker, M., Parker, D., Rüde, E., Hamann, R., Uhlig, A., ... & Lien, R. (2011). Engineering failure analysis and design optimisation with HiP-HOPS. Engineering Failure Analysis, 18(2), 590-608. Lisnianski, A., & Levitin, G. (2003). Multi-state system reliability: assessment, optimization and applications (Vol. 6). Zaitseva, E., & Levashenko, V. (2013). Multiple-valued logic mathematical approaches for multi-state system reliability analysis. Journal of Applied Logic, 11(3), 350-362. Rauzy, A. B. (2008). Guarded transition systems: a new states/events formalism for reliability studies. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 222(4), 495-505.

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Most relevant and most probable ones leading to the failure of the system

Background and motivation

4

Combinatorial models

  • Boolean formalisms
  • Multistate systems

Scenarios

that cause the failure

  • f system

that don’t cause the failure of system Minimal failure scenarios Non-minimal failure scenarios

(showing the least situations that the system fails) Cut sets Path sets Minimal cutsets Failure scenarios Non-failure scenarios ? Fault tree analysis, ...

Extended fault trees Multivalued logic appraoches Multivalued decision diagrams Universal generation functions ...

Existing tools Introduction

  • Background and motivation
  • Overview of PhD work

Main contributions Conclusion

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Overview of PhD work

5

Introduction

  • Background and motivation
  • Overview of PhD work

Main contributions Conclusion

Finite Degradation Structures (FDSs)

A unified framework of combinatorial models

1 2 3

  • Finite degradation structures (FDSs)
  • Operations of FDSs
  • Reliability/safety modeling by FDSs
  • Assessment of models and accessible results
  • Data structure: extended decision diagrams
  • Algorithms of calculating indicators
  • Modeling language: FDS-ML (textual language)
  • Software: LatticeX
  • Safety instrumented systems
  • Railway signal systems
  • Modeling of epistemic uncertainty
  • Interface between MBSE and MBSA

Interesting applications Theoretical development Computer-based implementation www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Theoretical development

6

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Algebraic foundation Modeling framework www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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SLIDE 7

Illustrative example

7 Safety Instrumented System (multistate)

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

According to the standard IEC 61508, the components of SIS may fail into different failure modes:

Extracted from ISO/TR12489 www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Illustrative example

8 Problems

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

  • In IEC 61508, the combination of different failure modes are ignored, because its occurrence

probability is often low.

  • But, low probability scenarios may be critical to system’s reliability and safety.
  • Some interesting scenarios are also ignored:
  • This channel is failed-

dangerously.

  • By the alarm, you “detect”,

to some extent, the failure

  • f valve.

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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SLIDE 9

Illustrative example

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Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Propose a modeling framework, called Finite Degradation Structures (FDSs), to support the modeling and the calculations for multistate systems. Models

Scenarios Probabilistic indicators

System

Modeling Calculation

Indicators

Finite Degradation Structures (FDSs)

Multistate Multistate Multistate Critical scenarios:

  • Minimal scenarios
  • Maximal scenarios

Our solution

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Finite degradation structures (FDSs)

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Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Formal definition

FDS Assign a probability measure 𝑞 𝑞 𝐺𝑒𝑣, 𝑢 = 𝑔

𝐺𝑒𝑣 𝑢, …

∈ 0,1 𝑞 𝐺𝑡, 𝑢 = 𝑔

𝐺𝑡 𝑢, …

∈ 0,1 𝑞 𝐺𝑒𝑒, 𝑢 = 𝑔

𝐺𝑒𝑒 𝑢, …

∈ 0,1 𝑞 𝑋, 𝑢 = 𝑔

𝑥 𝑢, …

∈ 0,1

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Finite degradation structures (FDSs)

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Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Formal definition

FDS www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Operations on FDSs

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Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

▪ Operations are used to describe the relation between components, i.e. how the failure of components may lead to failure of the system. ▪ The operations on FDSs are defined as surjective mappings:

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Operations on FDSs

13 Monoidal product

⨂

Achieve the composition

  • f the state spaces of

different components. Cartesian product of sets Product order Product measure Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Operations on FDSs

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Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

=

Domain (product FDS)

(Discrete surjective mapping)

Codomain (FDS)

Monoidal product Monoidal product

⨂

Achieve the composition

  • f the state spaces of

different components.

  • peration

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Operations on FDSs

15 Operations for safety instrumented system

Notations

(Operator and variables)

Truth tables

(valuation of the operation) (Hasse diagram)

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

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Operations on FDSs

16 Minimal & maximal scenarios (local)

Minimal

state combinations

  • f reaching an

undesired state

Maximal

state combinations

  • f staying in an

acceptable state Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Reliability modeling using FDSs

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Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Modeling framework www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Reliability modeling using FDSs

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Syntax

Well-formed formulas

 Boolean equations

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Finite degradation model Semantics

Operations on FDSs

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Reliability modeling using FDSs

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Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Finite Degradation Model

(Expression tree)

𝑇𝑧𝑡𝑢𝑓𝑛 𝑇𝐷1 𝑇𝐷2 𝐻𝑇 𝐻𝑊

⟺

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Accessible results

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Probabilistic indicators

State probability:

Scenarios

Set of scenarios: Minimal & maximal scenarios: Conditional probability: Conditional scenarios: Sensitivity:

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Accessible results

21

Finite Degradation Model

(Expression tree)

𝑇𝑧𝑡𝑢𝑓𝑛 𝑇𝐷1 𝑇𝐷2 𝐻𝑇 𝐻𝑊

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Scenarios

Degradation orders can propagate bottom-up through the operations in the model.

Probabilistic indicators

Probabilities can propagate bottom-up through the

  • perations in the model.

Inputs

FDSs equipped with probability distributions at component level. www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Inputs

FDSs equipped with probability distributions at component level.

Accessible results

22

Finite Degradation Model

(Expression tree)

𝑇𝑧𝑡𝑢𝑓𝑛 𝑇𝐷1 𝑇𝐷2 𝐻𝑇 𝐻𝑊

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Scenarios

Degradation orders can propagate bottom-up through the operations in the model.

Probabilistic indicators

Probabilities can propagate bottom-up through the

  • perations in the model.

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Accessible results

23

Finite Degradation Model

(Expression tree)

𝑇𝑧𝑡𝑢𝑓𝑛 𝑇𝐷1 𝑇𝐷2 𝐻𝑇 𝐻𝑊

C_s: a set of conditions that limit the valuation of certain state variables. Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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SLIDE 24

Inputs

FDSs equipped with probability distributions at component level.

Accessible results

24

Finite Degradation Model

(Expression tree)

𝑇𝑧𝑡𝑢𝑓𝑛 𝑇𝐷1 𝑇𝐷2 𝐻𝑇 𝐻𝑊

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Probabilistic indicators

Probabilities can propagate bottom-up through the

  • perations in the model.

Scenarios

Degradation orders can propagate bottom-up through the operations in the model. www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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SLIDE 25

Accessible results

25

Finite Degradation Model

(Expression tree)

𝑇𝑧𝑡𝑢𝑓𝑛 𝑇𝐷1 𝑇𝐷2 𝐻𝑇 𝐻𝑊

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Scenarios

▪ Maximal scenarios of 𝑇𝑧𝑡𝑢𝑓𝑛 = 𝑋 ▪ Minimal scenarios of 𝑇𝑧𝑡𝑢𝑓𝑛 = 𝐺𝑒𝑒

The combination of different failure modes appears in minimal scenarios.

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Computer-based implementation

26

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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SLIDE 27

Computer-based implementation

27

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

FDS-ML: textual modeling language for designing finite degradation models LatticeX: a small tool developed in Python to perform the required calculations www.ntnu.no PhD Defense – June 2nd 2020, NTNU

Yang, L., & Rauzy, A. (2019, October). FDS-ML: A New Modeling Formalism for Probabilistic Risk and Safety Analyses. In International Symposium on Model-Based Safety and Assessment (pp. 78-92). Springer, Cham.

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Interesting applications

28

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Modeling of epistemic uncertainty

Epistemic uncertainty: The state of component/system becomes uncertain due to the lack of detections. www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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SLIDE 29

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Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

Interesting applications

FDSs as interface between MBSA and MBSE

MBSE (Model-Based Systems Engineering) MBSA (Model-Based Safety Assessment)

Synchronize ▪ Structural behavior (hierarchical decomposition) ▪ Functional behavior (states and mappings) www.ntnu.no PhD Defense – June 2nd 2020, NTNU

Yang, L., Rauzy, A., & Haskins, C. (2018, October). Finite degradation structures: a formal framework to support the interface between MBSE and MBSA. In 2018 IEEE International Systems Engineering Symposium (ISSE) (pp. 1-6). IEEE.

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Conclusion

30

Introduction Main contributions

  • Theoretical development

Illustrative example Finite degradation structures (FDSs) Operations on FDSs Reliability modeling using FDSs Accessible results

  • Computer-based implementation
  • Interesting applications

Modeling of epistemic uncertainty FDSs as interface between MBSA and MBSE

Conclusion

❑ We propose a modeling framework, called finite degradation structures (FDSs), seen as the unified framework of reliability combinatorial models for both Boolean and multistate systems. ❑ The most highlighted part of FDSs is the extension of the notion of minimal cut/path sets into multistate systems, i.e. as minimal/maximal scenarios. Future works:

  • Completing the theoretical framework, including the calculation of importance

measures for multistate systems [Zaitseva 2012], the coherency problems, etc.

  • Enlarging the modeling library
  • Improving the efficiency of the calculation algorithms [Rauzy 2019]
  • Upgrading the software LatticeX

Zaitseva, E. (2012). Importance analysis of a multi-state system based on multiple-valued logic methods. In Recent Advances in System Reliability (pp. 113-134). Springer, London. Rauzy, A., & Yang, L. (2019). Decision Diagram Algorithms to Extract Minimal Cutsets of Finite Degradation Models. Information, 10(12), 368.

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

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Thanks.

www.ntnu.no PhD Defense – June 2nd 2020, NTNU

Academic publications

31

  • 1. Reliability modeling using finite degradation structures

(Conference paper) Liu Yang and Antoine Rauzy 3rd International Conference on System Reliability and Safety (ICSRS 2018), Barcelona, November 2018

  • 2. Finite degradation structures: a formal framework to

support the interface between MBSE and MBSA

(Conference paper) Liu Yang, Antoine Rauzy and Cecilia Haskins 2018 IEEE International Systems Engineering Symposium (ISSE), Rome, October 2018

  • 3. Reliability assessment of phased-mission systems with

AltaRica 3.0

(Conference paper) Michel Batteux, Tatiana Prosvirnova, Antoine Rauzy and Liu Yang 29th European Safety and Reliability Conference (ESREL 2019), Hanover, September 2019

  • 4. Finite degradation analysis of multiple safety instrumented

systems

(Conference paper) Liu Yang, Antoine Rauzy and Mary Ann Lundteigen 29th European Safety and Reliability Conference (ESREL 2019), Hanover, September 2019

  • 5. FDS-ML: a new modeling formalism for probabilistic risk

and safety analyses

(Conference paper) Liu Yang and Antoine Rauzy 6th International Symposium on Model-Based Safety and Assessment (IMBSA 2019), Thessaloniki, October 2019

  • 6. Model synthesis using Boolean expression diagrams

(Journal paper) Liu Yang and Antoine Rauzy Reliability Engineering & System Safety, 2019.

  • 7. Finite degradation structures

Antoine Rauzy and Liu Yang Journal of Applied Logic, November 2019.

  • 8. Decision diagram algorithms to extract minimal cutsets
  • f finite degradation models

Antoine Rauzy and Liu Yang Information, November 2019.

  • 9. Epistemic space of degradation processes

Liu Yang and Antoine Rauzy Under review by Journal of Applied Non-Classical Logics, submitted in July 2019.