Competing Failure Risk Analysis Using Dempster-Shafer Theory

Safety systems are important components of high consequence systems that are intended to prevent the unintended operation of the system and thus the potentially significant negative consequences that could result from such operation. This presentation investigates and illustrates formal procedures for assessing the uncertainty in the probability that a safety system will fail to operate as intended in an accident environment. Probability theory and evidence theory are introduced as possible mathematical structures for the representation of the epistemic uncertainty associated with the performance of safety systems, and a representation of this type is illustrated with a hypothetical safety system involving one weak link and one strong link that is exposed to a high temperature fire environment. Topics considered include: (i) the nature of diffuse uncertainty information involving a system and its environment, (ii) the conversion of diffuse uncertainty information into the mathematical structures associated with probability theory and evidence theory, and (iii) the propagation of these uncertainty structures through a model for a safety system to obtain representations in the context of probability theory and evidence theory of the uncertainty in the probability that the safety system will fail to operate as intended. The results suggest that evidence theory provides a potentially valuable representational tool for the display of the implications of significant epistemic uncertainty in inputs to complex analyses. *†‡

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