General failure probability assessment for multi-mode system with fuzzy-random variables by improved line sampling

Normalizing the measurement of basic variable space, the general failure probability where the basic variable possesses both fuzzy uncertainty and random uncertainty, called fuzzy-random variable, simultaneously is defined. In the calculation of the defined general failure probability, the fuzzy-random variable is transformed into a random variable equivalently, and then the general failure probability is transformed into an equivalent random failure probability. As both probability density function (PDF) describing the randomness and membership function describing the fuzziness of the fuzzy-random variable are normal, the formulation and parameters of the equivalent PDF are derived in this contribution. Adaptive line sampling method is employed to assess the general failure probability of the structural system with multiple failure modes. The numerical examples demonstrate the precision and the efficiency of the adaptive line sampling based on the general failure probability assessment.