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Reliability analysis of structural system with multiple failure modes and mixed uncertain input variables

In the design of engineering structure, uncertainties can be modeled as randomness or fuzziness depending on the amount of information available. In this article, the estimation of failure probability of structural system with multiple failure modes and mixed (random and fuzzy) inputs is considered. We firstly review the addition law of failure probability and a linear programming based bound method, and then these two techniques are combined to deal with structural system with multiple failure modes and only random inputs. Eventually, this method is extended for estimating the membership function of the failure probability of structural system with both random and fuzzy inputs. This method is computationally cheap, especially for the structural system with a large number of failure modes. Several numerical examples are introduced for demonstrating the efficiency and accuracy of the proposed method.