Reliability measure and its solution based on random and fuzzy distribution parameters

The distribution parameters of random variables are often treated as random interval variable due to insufficient information in engineering. Based on the interval distribution parameters, a new reliability measure is proposed and analyzed. Some direct and indirect methods are given to solve the new reliability measure. Furthermore, a new reliability index is defined and analyzed for fuzzy distribution parameters. At last, some practicable examples are taken to testify rationality of the new reliability measures and the accuracy of the given solutions.