Probability model of random reliability exceeding reference value under uncertain random distribution parameters

In case that uncertain distribution parameters are random, the traditional reliability is random as well. For the problem with uncertainty distribution parameters, a new reliability index is established on the probability that reflects the random reliability is smaller than the reference one. The new model can reflect the failure probability of the structure objectively under the uncertain distribution parameters. The detailed implementation of the solutions of the new reliability index are presented on the available three point estimation. Comparing with the universal numerical simulation, the three point estimation based methods for the new reliability index possess higher efficiency under the acceptable precision comparing with the analytical method.The three point estimation based methods require neither iteration nor gradient so that they can be applied in the complex problems. Some samples are given to explain the rationality of the model and validate their precision and efficiency.