Towards Probabilistic Modelling in Event-B

Event-B provides us with a powerful framework for correct-by-construction system development. However, while developing dependable systems we should not only guarantee their functional correctness but also quantitatively assess their dependability attributes. In this paper we investigate how to conduct probabilistic assessment of reliability of control systems modeled in Event-B. We show how to transform an Event-B model into a Markov model amendable for probabilistic reliability analysis. Our approach enables integration of reasoning about correctness with quantitative analysis of reliability.

[1]  Cliff B. Jones,et al.  RODIN (Rigorous Open Development Environment for Complex Systems) , 2005 .

[2]  Graeme Smith,et al.  A Stepwise Development Process for Reasoning About the Reliability of Real-Time Systems , 2007, IFM.

[3]  P. O'Connor,et al.  Practical Reliability Engineering , 1981 .

[4]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[5]  Ralph-Johan Back,et al.  Generalizing Action Systems to Hybrid Systems , 1999, FTRTFT.

[6]  Thai Son Hoang,et al.  Qualitative Probabilistic Modelling in Event-B , 2007, IFM.

[7]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..

[8]  Annabelle McIver,et al.  The probabilistic steam boiler: a case study in probabilistic data refinement , 1998 .

[9]  Daniel R. Eno.  Practical Reliability Engineering, 4th Ed. , 2003 .

[10]  Neil R. Storey,et al.  Safety-critical computer systems , 1996 .

[11]  Marta Kwiatkowska,et al.  Controller Dependability Analysis by Probabilistic Model Checking , 2004 .

[12]  Joost-Pieter Katoen,et al.  A Markov reward model checker , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[13]  Jean-Raymond Abrial,et al.  The B-book - assigning programs to meanings , 1996 .

[14]  Christel Baier,et al.  Principles of model checking , 2008 .

[15]  D. Craigen,et al.  Case study: Traffic Alert and Collision-Avoidance System , 1994, IEEE Software.

[16]  John G. Kemeny,et al.  Finite Markov Chains. , 1960 .

[17]  Hans A. Hansson.  Time and probability in formal design of distributed systems , 1991, DoCS.

[18]  Christel Baier,et al.  Principles of Model Checking (Representation and Mind Series) , 2008 .

[19]  Annabelle McIver,et al.  Abstraction, Refinement and Proof for Probabilistic Systems , 2004, Monographs in Computer Science.

[20]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[21]  D. Craigen,et al.  Case study: Paris Metro Signaling System , 1994, IEEE Software.

[22]  Joost-Pieter Katoen,et al.  A probabilistic extension of UML statecharts: Specification and Verification. , 2002 .

[23]  Marta Z. Kwiatkowska.  Quantitative verification: models, techniques and tools , 2007, ESEC/SIGSOFT FSE.