The use of multilegged arguments to increase confidence in safety claims for software-based systems: A study based on a BBN analysis of an idealized example

The work described here concerns the use of so-called multi-legged arguments to support dependability claims about software-based systems. The informal justification for the use of multi-legged arguments is similar to that used to support the use of multi-version software in pursuit of high reliability or safety. Just as a diverse, 1-out-of-2 system might be expected to be more reliable than each of its two component versions, so a two-legged argument might be expected to give greater confidence in the correctness of a dependability claim (e.g. a safety claim) than would either of the argument legs alone. Our intention here is to treat these argument structures formally, in particular by presenting a formal probabilistic treatment of ‘confidence’, which will be used as a measure of efficacy. This will enable claims for the efficacy of the multi-legged approach to be made quantitatively, answering questions such as ‘How much extra confidence about a system’s safety will I have if I add a verification argument leg to an argument leg based upon statistical testing?’ For this initial study, we concentrate on a simplified and idealized example of a safety system in which interest centres upon a claim about the probability of failure on demand. Our approach is to build a BBN (“Bayesian Belief Network”) model of a two-legged argument, and manipulate this analytically via parameters that define its node probability tables. The aim here is to obtain greater insight than is afforded by the more usual BBN treatment, which involves merely numerical manipulation. We show that the addition of a diverse second argument leg can, indeed, increase confidence in a dependability claim: in a reasonably plausible example the doubt in the claim is reduced to one third of the doubt present in the original single leg. However, we also show that there can be some unexpected and counter-intuitive subtleties here; for example an entirely supportive second leg can sometimes undermine an original argument, resulting overall in less confidence than came from this original argument. Our results are neutral on the issue of whether such difficulties will arise in real life - i.e. when real experts judge real systems