Citation: Littlewood, B. & Povyakalo, A. A. (2013). Conservative bounds for the pfd of a 1-out-of-2 software-based system based on an assessor's subjective probability of "not worse than independence". IEEE Transactions on Software Engineering, 39(12), pp. 1641 -1653 . doi: 10.1109 /TSE.2013 This is the accepted version of the paper.This version of the publication may differ from the final published version. Copyright and reuse: City Research Online aims to make research outputs of City, University of London available to a wider audience. Copyright and Moral Rights remain with the author(s) and/or copyright holders. URLs from City Research Online may be freely distributed and linked to. City Research Online: http://openaccess.city.ac.uk/ publications@city.ac.uk
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City Research OnlineConservative bounds for the pfd of a 1-out-of-2 softwarebased system based on an assessor's subjective probability of "not worse than independence"Bev Littlewood, Andrey PovyakaloCentre for Software Reliability, City University, London EC1V 0HB
AbstractWe consider the problem of assessing the reliability of a 1-out-of-2 software-based system, in which failures of the two channels cannot be assumed to be independent with certainty. An informal approach to this problem assesses the channel pfds (probabilities of failure on demand) conservatively and then multiplies these together in the hope that the conservatism will be sufficient to overcome any possible dependence between the channel failures. Our intention here is to place this kind of reasoning on a formal footing. We introduce a notion of "not worse than independence" and assume that an assessor has a prior belief about this, expressed as a probability. We obtain a conservative prior system pfd, and show how a conservative posterior system pfd can be obtained following the observation of a number of demands without system failure. We present some illustrative numerical examples, discuss some of the difficulties involved in this way of reasoning, and suggest some avenues of future research.KEY WORDS: System reliability; Software fault tolerance; 1-out-of-2 system; Dependent failures; Subjective probability.
BackgroundWe consider the problem of assessing the reliability of a 1-out-of-2 system in which the two software-based channels are "diverse" as a result of having been developed independently of one another (indeed, their designs may have been forced to be diverse by imposing diverse development procedures upon their designers). Such design-diverse fault tolerant systems have been used successfully in some safety critical applications: see (Littlewood, Popov et al. 2002;Wood, Belles et al. 2010).Whilst there is some general evidence that this kind of design-diverse fault tolerance is a good way of achieving high reliability -for example from experiments -there are serious difficulties in assessing the reliability of a particular system. An important problem arises from the fact that we can never be certain that the channels in such a system will fail...