A Qualitative Counterpart of Belief Functions with Application to Uncertainty Propagation in Safety Cases

Abstract

Critical systems such as those developed in the aerospace, railway or automotive industries need official documents to certify their safety via convincing arguments. However, informal tools used in certification documents seldom cover the uncertainty that pervades safety cases. Several works use quantitative approaches based on belief functions to model and propagate confidence/uncertainty in the argument structures (particularly those using goal structuring notation). However the numerical uncertainty information is often a naive encoding of qualitative expert inputs. In this paper, we outline a qualitative substitute to Dempster-Shafer theory and suggest new qualitative confidence propagation models. We also propose a more faithful encoding of expert inputs.

Confidence assessment in safety argument structure - Quantitative vs. qualitative approaches

“…and simplify the calculation of the terms: 13, we replace them by the sum of m 1 (p 1 ∧ C) and m 2 (p 2 ∧ C) from which we subtract the masses of the empty intersection and the redundant term…”

“…Furthermore, the reverse transformation back to the qualitative, using the elicitation model, can also introduce additional uncertainty to the argument. For these reasons and more listed in this paper, investigating an approach with a qualitative (as in [13]) counterpart of belief functions seems promising, both for uncertainty propagation and expert elicitation.…”