Risk assessment based on weak information using belief functions: a case study in water treatment

Whereas probability theory has been very successful as a conceptual framework for risk analysis in many areas where a lot of experimental data and expert knowledge are available, it presents certain limitations in applications where only weak information can be obtained. One such application investigated in this paper is water treatment, a domain in which key information such as input water characteristics and failure rates of various chemical processes is often lacking. An approach to handle such problems is proposed, based on the Dempster-Shafer theory of belief functions. Belief functions are used to describe expert knowledge of treatment process efficiency, failure rates, and latency times, as well as statistical data regarding input water quality. Evidential reasoning provides mechanisms to combine this information and assess the plausibility of various noncompliance scenarios. This methodology is shown to boil down to the probabilistic one where data of sufficient quality are available. This case study shows that belief function theory may be considered as a valuable framework for risk analysis studies in ill-structured or poorly informed application domains