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Uncertainties widely exist in practical engineering problems, which are often related to the material property, bounding condition, load, etc.With the intensive requirements of high product quality and reliability, understanding, identifying and controlling various uncertainties have become imperative.Uncertainty can also be viewed as the difference between the present knowledge and the complete knowledge, and according to this it can be classified into aleatory and epistemic types.Due to the flexibility in uncertainty description, evidence theory has been used to solve epistemic uncertainty recently and some exploratory work has been reported.However, until now evidence theory was barely used in complex engineering problems, and one main difficulty is the computational cost.Unlike the probability density function (PDF), an explicit function of the given imprecise information is unavailable in evidence theory.Since an evidence variable is given with a number of discontinuous sets rather than a smooth and continuous explicit function, a combination explosion might be inevitable for a multidimensional problem when using the evidence theory to conduct a reliability analysis.A new reliability analysis technique based on evidence theory which can greatly reduces the computational cost is developed in this paper.The computational scheme of the proposed technique can be illustrated in Figure 1.In the first step, the interval reliability analysis approach is introduced to obtain a non-probabilistie reliability index and a design point, based on which an assistant area can be created.For focal elements totally contained in this assistant area, there is no need of the extreme analysis for them.Through such a treatment, we can greatly reduce the focal elements that need to conduct the time-consuming extreme analysis.In the second step, for a focal element needing extreme analysis, the interval analysis is adopted to efficiently obtain the bounds of the limit-state function within this element.A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure.The presented method is applied to a vehicle side impact crashworthiness problem under geometric and material uncertainty.