Reliability model involving fuzzy distribution parameters and its moment estimation

In case that available information is not sufficient to determine distribution parameters, fuzzy numbers can be used to describe the distribution parameters. For fuzzy distribution parameters, a new reliability measure model is established on characteristic value analysis, and the solutions of the model are proposed. Firstly, universal numerical simulation is introduced to estimate the new reliability measure. The universal numerical simulation is simple in concept and easy in implementation, and its solution converges to the real value. However, the efficiency of this method is low. In order to improve the efficiency, a single loop moment method and a double loop moment method are presented to estimate the new reliability measure based on the available three-point estimation. 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, the efficiency and the precision of the presented solutions. Comparing with the universal numerical simulation, the single loop moment method and the 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, so they can be conveniently applied to the reliability analysis involving fuzzy distribution parameters.