Comparison of Probabilistic and Possibility Theory-Based Methods for Design Against Catastrophic Failure Under Uncertainty

This paper compares probabilistic and possibility-based methods for design against catastrophic failure under uncertainty. It studies the effect of the amount of information on the effectiveness of each method. The study is confined to problems where the boundary between survival and failure is sharp. First, the paper examines the theoretical foundations of probability and possibility. It also compares the two methods when they are used to assess the risk of a system. Finally, it compares the two methods on two design problems. A major difference between probability and possibility is in the axioms about the union of events. Because of this difference, probability and possibility calculi are fundamentally different and one cannot simulate possibility calculus using probabilistic models. It is shown that possibility-based methods can be less conservative than probability-based methods in systems with many failure modes. On the other hand, possibility-based methods tend to be more conservative than probability-based methods in systems that fail only if many unfavorable events occur simultaneously. Probabilistic methods are better than possibility-based methods if sufficient information is available. However, the latter can be better if little information is available. A principal reason is that it is easier to identify the most conservative possibilistic model than the most conservative probabilistic model that is consistent with the available information.