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Modeling the probability of failure on demand (pfd) of a 1-out-of-2 system in which one channel is “quasi-perfect”

Zhao, X., Littlewood, B., Povyakalo, A. A. , Strigini, L. & Wright, D. (2017). Modeling the probability of failure on demand (pfd) of a 1-out-of-2 system in which one channel is “quasi-perfect”. Reliability Engineering & System Safety, 158, pp. 230-245. doi: 10.1016/j.ress.2016.09.002


Our earlier work proposed ways of overcoming some of the difficulties of lack of independence in reliability modeling of 1-out-of-2 software-based systems. Firstly, it is well known that aleatory independence between the failures of two channels A and B cannot be assumed, so system pfd is not a simple product of channel pfds. However, it has been shown that the probability of system failure can be bounded conservatively by a simple product of pfdA and pnpB (probability not perfect) in those special cases where channel B is sufficiently simple to be possibly perfect. Whilst this “solves” the problem of aleatory dependence, the issue of epistemic dependence remains: An assessor’s beliefs about unknown pfdA and pnpB will not have them independent. Recent work has partially overcome this problem by requiring only marginal beliefs – at the price of further conservatism. Here we generalize these results. Instead of “perfection” we introduce the notion of “quasi-perfection”: a small pfd practically equivalent to perfection (e.g. yielding very small chance of failure in the entire life of a fleet of systems). We present a conservative argument supporting claims about system pfd. We propose further work, e.g. to conduct “what if?” calculations to understand exactly how conservative our approach might be in practice, and suggest further simplifications.

Publication Type: Article
Additional Information: Copyright Elsevier 2016. Available under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence.
Publisher Keywords: Fault-free software; Program perfection; Quasi-perfection; Probability of perfection; 1-out-of-2 system reliability; Software diversity
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology > Computer Science > Software Reliability
Text - Accepted Version
Available under License : See the attached licence file.

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