In recent work we have argued for a formal treatment of confidence about the claims made in dependability cases for software-based systems. The key idea underlying this work is 'the inevitability of uncertainty': it is rarely possible to assert that a claim about safety or reliability is true with certainty. Much of this uncertainty is epistemic in nature, so it seems inevitable that expert judgment will continue to play an important role in dependability cases. Here we consider a simple case where an expert makes a claim about the probability of failure on demand (pfd) of a sub-system of a wider system, and is able to express his confidence about that claim probabilistically. An important, but difficult, problem then is how such sub-system (claim, confidence) pairs can be propagated through a dependability case for a wider system, of which the sub-systems are components. An informal way forward is to justify, at high confidence, a strong claim, and then conservatively only claim something much weaker: "I'm 99% confident that the pfd is less than 10 -5 , so it's reasonable to be 100% confident that it is less than 10 -3 ." These conservative pfds of sub-systems can then be propagated simply through the dependability case of the wider system. In this paper we provide formal support for such reasoning.
Abstract. Many software development practices aim at ensuring that software is correct, or fault-free. In safety critical applications, requirements are in terms of probabilities of certain behaviours, e.g. as associated to the Safety Integrity Levels of IEC 61508. The two forms of reasoning -about evidence of correctness and about probabilities of certain failures -are rarely brought together explicitly. The desirability of using claims of correctness has been argued by many authors, but not been taken up in practice. We address how to combine evidence concerning probability of failure together with evidence pertaining to likelihood of fault-freeness, in a Bayesian framework. We present novel results to make this approach practical, by guaranteeing reliability predictions that are conservative (err on the side of pessimism), despite the difficulty of stating prior probability distributions for reliability parameters. This approach seems suitable for practical application to assessment of certain classes of safety critical systems.
Background. Computer aids can affect decisions in complex ways, potentially even making them worse; common assessment methods may miss these effects. We developed a method for estimating the quality of decisions, as well as how computer aids affect it, and applied it to computer-aided detection (CAD) of cancer, reanalyzing data from a published study where 50 professionals (“readers”) interpreted 180 mammograms, both with and without computer support. Method. We used stepwise regression to estimate how CAD affected the probability of a reader making a correct screening decision on a patient with cancer (sensitivity), thereby taking into account the effects of the difficulty of the cancer (proportion of readers who missed it) and the reader’s discriminating ability (Youden’s determinant). Using regression estimates, we obtained thresholds for classifying a posteriori the cases (by difficulty) and the readers (by discriminating ability). Results. Use of CAD was associated with a 0.016 increase in sensitivity (95% confidence interval [CI], 0.003–0.028) for the 44 least discriminating radiologists for 45 relatively easy, mostly CAD-detected cancers. However, for the 6 most discriminating radiologists, with CAD, sensitivity decreased by 0.145 (95% CI, 0.034–0.257) for the 15 relatively difficult cancers. Conclusions. Our exploratory analysis method reveals unexpected effects. It indicates that, despite the original study detecting no significant average effect, CAD helped the less discriminating readers but hindered the more discriminating readers. Such differential effects, although subtle, may be clinically significant and important for improving both computer algorithms and protocols for their use. They should be assessed when evaluating CAD and similar warning systems.
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