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To avoid the shortages and limitations of probabilistic and non-probabilistic reliability model for structural reliability analysis in the case of limited samples for basic variables, a new imprecise probability model is proposed. Confidence interval with a given confidence is calculated on the basis of small samples by gray theory, which is not depending on the distribution pattern of variable. Then basic probability assignments and focal elements are constructed and approximation methods of structural reliability based on belief and plausibility functions are proposed in the situation that structure limit state function is monotonic and non-monotonic, respectively. The numerical examples show that the new reliability model utilizes all the information included in small samples and considers both aleatory and epistemic uncertainties in them, thus it can rationally measure the safety of the structure and the measurement can be more and more accurate with the increasing of sample size.

An Imprecise Probability Model for Structural Reliability Based on Evidence and Gray Theory