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An algebra of temporal faults

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Abstract

Faults modelling is essential to anticipate failures in critical systems. Traditionally, Static Fault Trees are employed to this end, but Temporal and Dynamic Fault Trees are gaining evidence due to their enriched power to model and detect intricate propagation of faults that lead to a failure. In previous work, we showed a strategy based on the process algebra CSP and Simulink models to obtain fault traces that lead to a failure. Although that work used Static Fault Trees, it could be used with Temporal or Dynamic Fault Trees. In the present work we define an algebra of temporal faults (with a notion of fault propagation) and prove that it is indeed a Boolean algebra. This allows us to inherit Boolean algebra’s properties, laws and existing reduction techniques, which are very beneficial for faults modelling and analysis. We illustrate our work on a simple but real case study supplied by our industrial partner EMBRAER.

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Notes

  1. Pandora stands for: P-AND-ORA, which translates to Priority AND, Time.

  2. This variant “M” is the machine-readable version of CSP.

  3. The 2002 tutorial is reported in Nipkow et al. (2002), but there is a newer version published with the tool itself. The tool and the tutorial are available on their website at http://isabelle.in.tum.de.

  4. Whether a top event indeed causes a catastrophic or major failure is out of the scope of this paper; we consider that, if it is possible that such failure occurs, then it will.

  5. In our previous work we designed the observer to ignore order as well, by making similar traces—with different ordering—the same size. Here we modified the observer specification to make similar traces with different sizes.

  6. In this work we do not show the mapping function from traces to ATF (and the mapping function with XBefore in Section 4.2). The mapping rules follow the traces: XBefore is obtained by the order of occurrence and the absence of an event is the complement (−).

  7. In the final formula, \(\left (B {\cap } S {\cap } -A \right ) {\cup } \left (A {\cap } B {\cap } -S \right )\) is equivalent to \(\left (B {\cap } \left (S \oplus A \right ) \right )\). There is a typo in our previous work (Didier and Mota 2015). The expression was written with an OR (∨) but it should an XOR (⊕).

  8. http://www.ines.org.br

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Acknowledgments

We would like to thank Alexander Romanovsky, Zoe Andrews and Richard Payne for all discussions about fault modelling and dependability. We also thank the anonymous referees of FMi 2015 and ISF journal for comments in drafts of this work. This work was funded by CNPq, grants 476821/2011-8, 442859/2014-7, and 246956/2012-7, and by FACEPE grant IBPG-0408-1.03/11. This work was partially supported by the National Institute of Science and Technology for Software Engineering (INESFootnote 8), funded by CNPq and FACEPE, grants 573964/2008-4 and APQ-1037-1.03/08.

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  1. Av. Jornalista Anibal Fernandes, Cidade Universitária, s/n, ZIP 50740-560, Recife, PE, Brazil

    André Didier & Alexandre Mota

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  1. André Didier
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  2. Alexandre Mota
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Correspondence to André Didier.

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Didier, A., Mota, A. An algebra of temporal faults. Inf Syst Front 18, 967–980 (2016). https://doi.org/10.1007/s10796-016-9664-8

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