Abstract
Fault Tree Analysis has been a cornerstone of safety-critical systems for many years. It has seen various extensions to enable it to analyse dynamic behaviours exhibited by modern systems with redundant components. However, none of these extended FTA approaches provide much support for modelling situations where events have to be "nearly simultaneous", i.e., where events must occur within a certain interval to cause a failure. Although one such extension, Pandora, is unique in providing a "Simultaneous-AND" gate, it does not allow such intervals to be represented. In this work, we extend the Simultaneous-AND gate to include a parameterized interval – referred to as pSAND – such that the output event occurs if the input events occur within a defined period of time. This work then derives an expression for the exact quantification of pSAND for exponentially distributed events and provides an approximation using Monte Carlo simulation which can be used for other distributions.
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References
Gulati, R., Dugan, J.B.: A modular approach for analyzing static and dynamic fault trees. In: Reliability and Maintainability Symposium (1997)
Merle, G., Roussel, J.: Algebraic modelling of Fault Trees with Priority AND gates. In: 1st IFAC Workshop, pp. 175–180 (2007)
Dugan, J.B., Doyle, S.A.: New results in fault-tree analysis. In: Tutorial Notes of the Annual Reliability and Maintainability Symposium (1997)
Dugan, J.B., Bavuso, S.J., Boyd, M.A.: Dynamic fault-tree models for fault-tolerant computer systems. IEEE Transactions on Reliability 41(3), 363–377 (1992)
Walker, M., Papadopoulos, Y.: Synthesis and analysis of temporal fault trees with PANDORA 2: The time of Priority AND gates. Nonlinear Analysis: Hybrid Systems 2(2), 368–382 (2008)
Fussell, J.B., Aber, E.F., Rahl, R.G.: On the quantitative analysis of Priority-AND failure logic. IEEE Transactions on Reliability R-25(5), 324–326 (1976)
Walker, M., Papadopoulos, Y.: Pandora 2: The time of priority-OR gates. In: IFAC Workshop on Dependable Control of Discrete Event Systems (2007)
Walker, M.: Pandora: a logic for the qualitative analysis of temporal fault trees. Dissertation, University of Hull (2009)
Vesely, W.E., Stamatelatos, M., et al.: Fault tree handbook with aerospace applications. NASA Office of Safety and Mission Assurance, Washington DC (2002)
Durga, R., Gopika, V., et al.: Dynamic fault tree analysis using Monte Carlo simulation in probabilistic safety assessment. Reliability Engineering & System Safety 94(4), 872–883 (2009)
Yuge, T., Yanagi, S.: Quantitative analysis of a fault tree with Priority AND gates. Reliability Engineering & System Safety 93(11), 1577–1583 (2008)
Long, W., Sato, Y., Horigome, M.: Quantification of sequential failure logic for fault tree analysis. Reliability Engineering & System Safety 67(3), 269–274 (2000)
Edifor, E., Walker, M., Gordon, N.: Quantification of priority-OR gates in temporal fault trees. In: Ortmeier, F., Lipaczewski, M. (eds.) SAFECOMP 2012. LNCS, vol. 7612, pp. 99–110. Springer, Heidelberg (2012)
Merle, G., Roussel, J.: Probabilistic algebraic analysis of fault trees with priority dynamic gates and repeated events. IEEE Transactions on Reliability 59(1), 250–261 (2010)
Chaochen, Z., Hoare, C., Ravn, A.: A calculus of Durations. Information Processing Letters 40(5), 269–276 (1991)
Hansen, K.M., Anders, P.R., Stavridou, V.: From safety analysis to software requirements. IEEE Transactions on Software Engineering 24(7), 573–584 (1998)
Palshikar, G.: Temporal fault trees. Information and Software Technology 44(3), 137–150 (2002)
Gorski, J., Wardzinski, A.: Deriving real-time requirements for software from safety analysis. In: Real-Time Systems, pp. 9–14 (1996)
Schellhorn, G., Thums, A., Reif, W.: Formal fault tree semantics. In: Proceedings of The Sixth World Conference on Integrated Design & Process Technology (2002)
Güdemann, M., Ortmeier, F., Reif, W.: Computation of Ordered Minimal Critical Sets. In: Proceedings of the 7th Symposium on Formal Methods for Automation and Safety in Railway and Automotives (2008)
Babczyński, T., Lukowicz, M., Magott, J.: Time coordination of distance protections using probabilistic fault trees with time dependencies. IEEE Transactions on Power Delivery 25(3), 1402–1409 (2010)
Rocco, C., Muselli, M.: A machine learning algorithm to estimate minimal cut and path sets from a Monte Carlo simulation. In: Probabilistic Safety Assessment and Management (PSAM7–ESREL), pp. 3142–3147 (2004)
Chan, J.C., Kroese, D.P.: Rare-event probability estimation with conditional Monte Carlo. Annals of Operations Research 189(1), 43–61 (2009)
Wolfram Research, What Is Mathematica? (2013), http://www.wolfram.co.uk/mathematica (accessed January 07, 2013)
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Edifor, E., Walker, M., Gordon, N. (2013). Quantification of Simultaneous-AND Gates in Temporal Fault Trees. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds) New Results in Dependability and Computer Systems. Advances in Intelligent Systems and Computing, vol 224. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00945-2_13
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DOI: https://doi.org/10.1007/978-3-319-00945-2_13
Publisher Name: Springer, Heidelberg
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