Session 1: MBSA

 Session chair: David Parker

10:30 - 12:30 Wednesday 4th September 2013
10:30 Towards a unified definition of Minimal Cut Sequences
Authors: Pierre-Yves Chaux, Jean-Marc Roussel, Jean-Jacques Lesage, Gilles Deleuze, Marc Bouissou
Abstract: The growing complexity of systems makes the complexity of reliability model growing, implying the need to model both the dynamics of systems and the reparability of components. The qualitative reliability analyses aim at finding the minimal representation of all the scenarios of failures and repairs of the components, leading to the system failure. This minimal representation is the set of Minimal Cut Sequences. In order to provide a formal definition of these specific scenarios, whatever the risk analysis model used, this paper proposes coherency rules for dynamic and repairable systems  those dysfunctional scenarios are modeled by a finite automaton.
11:00 Introducing Temporal Behaviour into Binary Decision Diagrams
Authors: Ernest Edem Edifor, Martin Walker, Neil Gordon
Abstract: Binary Decision Diagrams (BDDs) are an alternative technique used in the analyses of safety-critical system fault trees. BDDs have been found to produce the exact top-event probability more efficiently by reducing computing resources drastically. Unfortunately, this efficient technique is not used in the analysis of fault trees featuring sequential ordering of events. However, in the real world, the sequential ordering of  events cannot be overlooked because it produces a more accurate evaluation of systems. We introduce a new technique, Temporal BDD (TBDD), that incorporates temporal behaviour – via Priority-AND gates – into BDDs. TBDD provides the exact results for both qualitative and quantitative analyses. However, unlike BDD, quantitative analyses cannot be performed on 'unminimised' cut sequences yet. It is hoped that this work will form the foundation for the full qualitative and quantitative analyses of Dynamic Fault Trees and Temporal Fault Trees in the near future. 
11:30 Preliminary System Safety Analysis with Limited Markov Chain Generation
Authors: Pierre-Antoine Brameret, Jean-Marc Roussel, Antoine Rauzy
Abstract: Markov chains are powerful and versatile tool to calculate reliability indicators.However, their use is limited for two reasons: the exponential blowup of the size of the model, and the difficulty to design models. To overcome this second difficulty, a solution consists in generating automatically the Markov chain from a higher level description, e.g. a stochastic Petri net or an AltaRica model. These higher level models describe the Markov chain implicitely.

In this article, we propose an algorithm to generate partial Markov chains. The idea is to accept a little loss of accuracy in order to reduce the size of the generated chain. The cornerstone of this method is a Relevance Factor associated to each state of the chain. This factor enables the selection of the most representative states. We show on an already published test case, that our method provides very accurate results while reducing dramatically the complexity of the assessment. It is worth noticing that the proposed method does not depend on any particular high-level modeling formalism. 
12:00 Using Coloured Petri Nets for integrated reliability and safety evaluations
Authors: Bruno Pinna, Genia Babykina, Nicolae Brinzei, Jean-Francois Petin
Abstract: Integrated Deterministic and Probabilistic Dependability Analysis (IDPDA) is respectively required for safety properties veri cation and reliability & availability assessment of critical systems. This paper presents an approach towards IDPDA using Coloured Petri Nets (CPN). Contributions are related to: (a) hierarchical modelling guidelines that cover deterministic and probabilistic features of a physical system under control, (b) coupling Monte-Carlo simulation with CPN model checking that requires a previous determinisation of the CPN stochastic model. Our approach is illustrated using a toy case study.