Combination of qualitative and quantitative sources of knowledge for risk assessment

This paper focuses on representation of the reliability of system in the framework of possibility theory. Particularly, given a (probabilistic) quantitative knowledge pertaining to the time to failure of a system (risk function) and some qualitative knowledge about the degree of pessimism and optimism about the information supplied by this quantitative knowledge, one may construct a possibilistic reliability function of the system. The latter models the possibility that the system survives up to the current time. The proposal is motivated by the observation that the system may fail even if the risk function considers this failure as unlikely. Besides, research from cognitive science shows that probability values, particularly when human factor is involved in the system tend to be overestimated. This methodology involves implicitly the combination of the two pieces of knowledge into a more refined knowledge expressed in the possibility framework. Several ramifications of the proposal, particularly considering the common exponential lifetime distribution will be investigated. On the other hand in the absence of any qualitative knowledge the proposal is straightforwardly related to the notion of probability-possibility transformations investigated in the fuzzy literature.