The Dynamic-to-Static Conversion of Dynamic Fault Trees Using Stochastic Dependency Graphs and Stochastic Activity Networks

Abstract

In this paper a new modeling framework for the dependability analysis of complex systems is presented and related to dynamic fault trees (DFTs). The methodology is based on a modular approach: two separate models are used to handle, the fault logic and the stochastic dependencies of the system. Thus, the fault schema, free of any dependency logic, can be easily evaluated, while the dependency schema allows the modeler to design new kind of non-trivial dependencies not easily caught by the traditional holistic methodologies. Moreover, the use of a dependency schema allows building a pure behavioral model that can be used for various kinds of dependability studies. In the paper is shown how to build and integrate the two modular models and convert them in a Stochastic Activity Network. Furthermore, based on the construction of the schema that embeds the stochastic dependencies, the procedure to convert DFTs into static fault trees is shown, allowing the resolution of DFTs in a very efficient way.

Cite this paper

G. Manno, F. Chiacchio and F. Pappalardo, "The Dynamic-to-Static Conversion of Dynamic Fault Trees Using Stochastic Dependency Graphs and Stochastic Activity Networks,"*Engineering*, Vol. 5 No. 2, 2013, pp. 157-166. doi: 10.4236/eng.2013.52023.

G. Manno, F. Chiacchio and F. Pappalardo, "The Dynamic-to-Static Conversion of Dynamic Fault Trees Using Stochastic Dependency Graphs and Stochastic Activity Networks,"

References

[1] J. B. Dugan and S. J. Bavuso, “Fault Trees and Sequence Dependencies,” Proceedings of Annual Reliability and Maintainability Symposium, Los Angeles, 23-25 January 1990, pp. 232-235. doi:10.1109/ARMS.1990.67971

[2] J. B. Dugan and S. J. Bavuso, “Dynamic Fault-Tree Models for Fault Tolerant Computer Systems,” IEEE Transactions on Reliability, Vol. 41, No. 3, 1992, pp. 363-377. doi:10.1109/24.159800

[3] S. Amari, G. Dill and E. Howald, “A New Approach to Solve Dynamic Fault Trees,” Annual Reliability and Maintainability Symposium, 2003, pp. 374-379.

[4] R. Gulati and J. B. Dugan, “A Modular Approach for Analyzing Static and Dynamic Fault Trees,” Proceedings of Annual Reliability and Maintainability Symposium, Philadelphia, 13-16 January 1997, pp. 57-63.
doi:10.1109/RAMS.1997.571665

[5] M. Lanus, L. Yin and K. S. Trivedi, “Hierarchical Composition and Aggregation of State-Based Availability and Performability Models,” IEEE Transactions on Reliability, Vol. 52, No. 1, 2003, pp. 44-52.
doi:10.1109/TR.2002.805781

[6] B. N. Feinberg and S. S. Chiu, “A Method to Calculate Steady-State Distributions of Large Markov Chains by Aggregating States,” Operations Research, Vol. 35, No. 2, 1987, pp. 282-290. doi:10.1287/opre.35.2.282

[7] M. Malhotra and K. S. Trivedi, “A Methodology for Formal Specification of Hierarchy in Model Solution,” Proceedings of 5th International Workshop Petri Nets and Performance Models, (PNPM-1993), Toulouse, 1922 October 1999, pp. 258-267.
doi:10.1109/PNPM.1993.393445

[8] S. Distefano andA. Puliafito, “Dynamic Reliability Block Diagrams vs Dynamic Fault Trees,” Proceedings of Annual Reliability and Maintainability Symposium RAMS’07, Orlando, 22-25 January 2007, pp. 71-76.

[9] A. Bobbio, L. Portinale, M. Minichino and E. Ciancamerla, “Improving the Analysis of Dependable Systems by Mapping Fault Trees into Bayesian Networks,” Reliability Engineering and System Safety, Vol. 71, No. 3, 2001, pp. 249-260. doi:10.1016/S0951-8320(00)00077-6

[10] H. Boudali and J. Dugan, “A New Bayesian Network Approach to Solve Dynamic Fault Trees,” Proceedings of Annual Reliability and Maintainability Symposium, Alexandria, 24-27 January 2005, pp. 451-456.
doi:10.1109/RAMS.2005.1408404

[11] H. Boudali and J. B. Dugan, “A Continuous-Time Bayesian Network Reliability Modeling, and Analysis Framework,” IEEE Transactions on Reliability, Vol. 55, No. 1, 2006, pp. 86-97. doi:10.1109/TR.2005.859228

[12] M. Bouissou and J. L. Bon, “A New Formalism That Combines Advantages of Fault-Trees and Markov Models: Boolean Logic Driven Markov Processes,” Relibility Engineering and System Safety, Vol. 82, No. 2, 2003, pp. 149-163. doi:10.1016/S0951-8320(03)00143-1

[13] S. Swaminathan and C. Smidts, “The Event Sequence Diagram Framework for Dynamic Probabilistic Risk Assessment,” Reliability Engineering and System Safety, Vol. 63, No. 1, 1999, pp. 73-90.
doi:10.1016/S0951-8320(98)00027-1

[14] D. Codetta-Raiteri, “The Conversion of Dynamic Fault Trees to Stochastic Petri Nets, as a case of Graph Transformation,” Electronic Notes in Electronic Computer Science, 127, No. 2, 2005, pp. 45-60.
doi:10.1016/j.entcs.2005.02.005

[15] V. Volovoi, “Modeling of System Reliability Petri Nets with Aging Tokens,” Reliability Engineering and System Safety, Vol. 84, No. 2, 2004, pp. 149-161.
doi:10.1016/j.ress.2003.10.013

[16] M. Marsaguerra, E. Zio, J. Devooght and P. E. Labeau, “A Concept Paper on dynamic Reliability via Monte Carlo Simulation,” Mathematics and Computers in Simulation, Vol. 47, No. 2-5, 1998, pp. 371-382.
doi:10.1016/S0378-4754(98)00112-8

[17] E. Zio, M. Marella and L. Podollini, “A Monte Carlo Simulation Approach to the Availability Assessment of Multi-State Systems with operational Dependencies,” Reliability Engineering and System Safety, Vol. 92, No. 7, 2007, pp. 871-882. doi:10.1016/j.ress.2006.04.024

[18] Mobius. http://www.mobius.illinois.edu/

[19] W. H. Sanders and J. F. Meyer, “Stochastic Activity Networks: Formal Definitions and Concepts,” In: H. Hermanns and J.-P. Katoen, Eds., Lectures on Formal Methods and Performance Analysis, Springer Verlag, Berlin, 2002, pp. 315-343.

[20] F. Chiacchio, D. D’Urso, N. Trapani, G. Manno and L. Compagno, “Dynamic Fault Trees Resolution: A Conscious Trade-Off between Analytical and Simulative Approaches,” Reliability Engineering and System Safety, Vol. 96, No. 11, 2011, pp. 1115-1126.
doi:10.1016/j.ress.2011.06.014

[21] G. Manno, F. Chiacchio, L. Compagno, D. D’Urso and N. Trapani, “Matcarlore: An Integrated FT and Monte Carlo Simulink Tool for the Reliability Assessment of Dynamic Fault Tree,” Expert Systems with Applications, Vol. 39, No. 12, 2012, pp. 10334-10342.
doi:10.1016/j.eswa.2011.12.020

[22] A. Rauzy, “Binary Decision Diagrams for Reliability Studies,” Handook of Performability Engineering, 2008, pp. 381-339.