A novel reliability model for random variables lacking sufficient probability information

In the case that sample data are insufficient to determine probability distributions of random variables, a novel reliability model is presented on the basis of evidence theory. For the original random variable with m sample data, a matching variable with (m+1) sample data is constructed and the (m+1) sample data form m sub-intervals that each sub-interval exactly only involves a sample datum of the original random variable, and then the basic probability assignment(BPA) for each sub-interval can be determined. For a failure mode of a structure with n-dimensional random variables, the BPAs of n-dimensional random variables can be synthesized by using the combination rule of Dempster, on which The belief measure of the structural failure F, Bel(F), and the plausibility measure of F, PI(F), can be uniquely determined. Further, the failure probability can be approximated by using Bel(F) and PI(F) as the upper and lower limits. The examples show that the presented model uses the information involved in the sample data sufficiently, thus it can rationally measure the safety of the structure.