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A conservative bound for the probability of failure of a 1-out-of-2 protection system with one hardware-only and one software-based protection train

Author

Listed:
  • Bishop, Peter
  • Bloomfield, Robin
  • Littlewood, Bev
  • Popov, Peter
  • Povyakalo, Andrey
  • Strigini, Lorenzo

Abstract

Redundancy and diversity have long been used as means to obtain high reliability in critical systems. While it is easy to show that, say, a 1-out-of-2 diverse system will be more reliable than each of its two individual “trains†, assessing the actual reliability of such systems can be difficult because the trains cannot be assumed to fail independently. If we cannot claim independence of train failures, the computation of system reliability is difficult, because we would need to know the probability of failure on demand (pfd) for every possible demand. These are unlikely to be known in the case of software. Claims for software often concern its marginalpfd, i.e. average across all possible demands. In this paper we consider the case of a 1-out-of-2 safety protection system in which one train contains software (and hardware), and the other train contains only hardware equipment. We show that a useful upper (i.e. conservative) bound can be obtained for the system pfd using only the unconditional pfd for software together with information about the variation of hardware failure probability across demands, which is likely to be known or estimatable. The worst-case result is obtained by “allocating†software failure probability among demand “classes†so as to maximize system pfd.

Suggested Citation

  • Bishop, Peter & Bloomfield, Robin & Littlewood, Bev & Popov, Peter & Povyakalo, Andrey & Strigini, Lorenzo, 2014. "A conservative bound for the probability of failure of a 1-out-of-2 protection system with one hardware-only and one software-based protection train," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 61-68.
  • Handle: RePEc:eee:reensy:v:130:y:2014:i:c:p:61-68
    DOI: 10.1016/j.ress.2014.04.002
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    References listed on IDEAS

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    1. Chris Garrett & George Apostolakis, 1999. "Context in the Risk Assessment of Digital Systems," Risk Analysis, John Wiley & Sons, vol. 19(1), pages 23-32, February.
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    Cited by:

    1. Bishop, Peter & Povyakalo, Andrey, 2020. "A conservative confidence bound for the probability of failure on demand of a software-based system based on failure-free tests of its components," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    2. Bishop, Peter & Povyakalo, Andrey, 2017. "Deriving a frequentist conservative confidence bound for probability of failure per demand for systems with different operational and test profiles," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 246-253.
    3. Yaguang Yang, 2019. "Test based safety-critical software reliability estimation using Bayesian method and flow network structure," Journal of Risk and Reliability, , vol. 233(5), pages 847-856, October.

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