An effective approach for probabilistic lifetime modelling based on the principle of maximum entropy with fractional moments

The paper presents a fractional moment method for probabilistic lifetime modelling of uncertain engineering systems. A novel feature of the method is the use of fractional moments, as opposed to integer moments commonly used so far in the structural reliability literature. The fractional moments are calculated from a small, simulated sample of remaining useful life of the system. And the fractional exponents that are used to model the system lifetime distribution are determined through the entropy maximization process, rather than assigned by an analyst in prior. Together with the theory of copula, the efficiency and accuracy of the proposed method are illustrated by the probabilistic lifetime modelling of several dynamical and discontinuous stochastic systems.