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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

Bishop, P. G., Bloomfield, R. E., Littlewood, B. , Popov, P. T., Povyakalo, A. A. & Strigini, L. (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 & System Safety, 130, pp. 61-68. doi: 10.1016/j.ress.2014.04.002


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.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Reliability Engineering & System Safety. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Reliability Engineering & System Safety, Volume 130, October 2014, Pages 61–68,
Publisher Keywords: Software reliability; Redundancy and diversity; Probability of failure on demand; 1-out-of-2 system; Protection system
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology > Computer Science > Software Reliability
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