Model and its point estimation for reliability involving uncertain distribution parameters

For engineering structure involving uncertain distribution parameters, a new reliability model based on characteristic value analysis is established, and the point estimation is employed to solve the model. In case of uncertain distribution parameters, the traditional failure probability becomes a random variable, and the failure probability of the structure should be remeasured from the mean and the standard deviation of the failure probability variable. After the concept of the new reliability model is described, the numerical simulation is proposed to estimate the new reliability measure, and a single loop moment method and double loop moment method are presented to estimate the new reliability measure based on the three-point estimation method. After the detailed implementations are described for the presented solutions of the model, several numerical and engineering samples are used to demonstrate the rationality of the model and the efficiency and the precision of the presented solutions. Comparing with the numerical simulation, a single loop moment method and double one possess higher efficiency for solving the new reliability measures, and moment based methods are easily to be implemented, in which neither iteration nor gradient is required, they can be conveniently applied to the reliability analysis involving uncertain distribution parameters.