Combined Probability-Possibility Evaluation Theory for Structural Reliability

In structural identification and planning, as pointed by Yao and Natke (1991), it is very important to evaluate the uncertainties of future loads and structural responses. In this paper, probability functions in which additive law holds are combined with possibility functions in which maxitive law holds, so that their evaluation measures belong to a kind of fuzzy measures instead of probability measures. By using their joint evaluation distributions and measures, one can evaluate the uncertain strength of parallel or serial structural systems and the survival or fracture possibility of structures. This paper presents some examples of case studies and shows that the proposed combined probability-possibility evaluation theory is effective to evaluate the combined objective and subjective reliability of structures from practical and theoretical points of view.