Abstract
Boolean-logic Driven Markov Processes (BDMPs) is a graphical language for reliability analysis of dynamic repairable systems. Simulation and trace-based analysis tools for BDMPs exist and have been used to analyze reliability, safety and security aspects of industrially relevant case studies. To enable a model-based analysis of BDMPs, such as probabilistic model checking, formal semantics is indispensable. This paper presents a rigorous semantics to repairable BDMPs using Markov automata (MA), a variant of continuous-time Markov chains (CTMCs) with action transitions. The semantics is modular: an MA is associated with each BDMP element and these are combined to obtain an automaton for the entire BDMP. By ignoring the actions that are used to “glue” the MA of BDMP elements, a CTMC is obtained that is amenable to analysis by e.g., model checking. We report on a prototypical implementation and experimentally show that our semantics corresponds to the BDMP interpretation by the tool Yet Another Monte Carlo Simulation.
S. Khan—Supported by a HEC-DAAD Scholarship.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Baier, C., de Alfaro, L., Forejt, V., Kwiatkowska, M.: Model checking probabilistic systems. In: Clarke, E., Henzinger, T., Veith, H., Bloem, R. (eds.) Handbook of Model Checking, pp. 963–999. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-10575-8_28
Bohnenkamp, H.C., D’Argenio, P.R., Hermanns, H., Katoen, J.P.: MODEST: a compositional modeling formalism for hard and softly timed systems. IEEE TSE 32(10), 812–830 (2006)
Boudali, H., Crouzen, P., Stoelinga, M.: A rigorous, compositional, and extensible framework for dynamic fault tree analysis. IEEE TDSC 7(2), 128–143 (2009)
Bouissou, M.: Automated dependability analysis of complex systems with the KB3 workbench: the experience of EDF R&D. In: ICEE. CIEM (2005)
Bouissou, M., Bon, J.L.: A new formalism that combines advantages of fault-trees and Markov models: Boolean logic driven Markov processes. Rel. Eng. Sys. Safety 82(2), 149–163 (2003)
Budde, C.E., Biagi, M., Monti, R.E., D’Argenio, P.R., Stoelinga, M.: Rare event simulation for non-Markovian repairable Fault Trees. TACAS 2020. LNCS, vol. 12078, pp. 463–482. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45190-5_26
Budde, C.E., Dehnert, C., Hahn, E.M., Hartmanns, A., Junges, S., Turrini, A.: JANI: quantitative model and tool interaction. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10206, pp. 151–168. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54580-5_9
Dehnert, C., Junges, S., Katoen, J.-P., Volk, M.: A Storm is coming: a modern probabilistic model checker. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017, Part II. LNCS, vol. 10427, pp. 592–600. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63390-9_31
Dugan, J.B., Bavuso, S.J., Boyd, M.A.: Dynamic fault-tree models for fault-tolerant computer systems. IEEE Trans. Reliab. 41(3), 363–377 (1992)
Eisentraut, C., Hermanns, H., Zhang, L.: On probabilistic automata in continuous time. In: LICS, pp. 342–351. IEEE Computer Society (2010)
Guck, D., Spel, J., Stoelinga, M.: DFTCalc: reliability centered maintenance via fault tree analysis (tool paper). In: Butler, M., Conchon, S., Zaïdi, F. (eds.) ICFEM 2015. LNCS, vol. 9407, pp. 304–311. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25423-4_19
Hartmanns, A., Hermanns, H.: A modest Markov automata tutorial. In: Krötzsch, M., Stepanova, D. (eds.) Reasoning Web. Explainable Artificial Intelligence. LNCS, vol. 11810, pp. 250–276. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-31423-1_8
Junges, S., Katoen, J.-P., Stoelinga, M., Volk, M.: One net fits all: a unifying semantics of Dynamic Fault Trees using GSPNs. In: Khomenko, V., Roux, O.H. (eds.) PETRI NETS 2018. LNCS, vol. 10877, pp. 272–293. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91268-4_14
Kaiser, B., Gramlich, C., Förster, M.: State/event fault trees - a safety analysis model for software-controlled systems. Rel. Eng. Sys. Safety 92, 1521–1537 (2007)
Kaiser, B., Liggesmeyer, P., Mäckel, O.: A new component concept for fault trees. In: SCS. CRPIT, vol. 33, pp. 37–46. Australian Computer Society (2003)
Marsan, M.A., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets, vol. 292. Wiley, New York (1995)
Piriou, P.Y., Faure, J.M., Lesage, J.J.: Generalized Boolean logic Driven Markov Processes: a powerful modeling framework for model-based safety analysis of dynamic repairable and reconfigurable systems. Rel. Eng. Sys. Safety 163, 57–68 (2017)
Ruijters, E., Stoelinga, M.: Fault tree analysis: a survey of the state-of-the-art in modeling, analysis and tools. Comput. Sci. Rev. 15, 29–62 (2015)
Volk, M., Junges, S., Katoen, J.P.: Fast dynamic fault tree analysis by model checking techniques. IEEE Trans. Ind. Inform. 14(1), 370–379 (2018)
Walker, M., Papadopoulos, Y.: Synthesis and analysis of temporal fault trees with PANDORA: the time of priority AND gates. Nonlinear Anal. Hybri. Syst. 2(2), 368–382 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Khan, S., Katoen, JP., Bouissou, M. (2020). A Compositional Semantics for Repairable BDMPs. In: Casimiro, A., Ortmeier, F., Bitsch, F., Ferreira, P. (eds) Computer Safety, Reliability, and Security. SAFECOMP 2020. Lecture Notes in Computer Science(), vol 12234. Springer, Cham. https://doi.org/10.1007/978-3-030-54549-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-54549-9_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-54548-2
Online ISBN: 978-3-030-54549-9
eBook Packages: Computer ScienceComputer Science (R0)