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

• Published in: Applied Mathematical Modelling 2017-11, Vol.51, p.626-642
• Main Authors: Zhang, Xufang, He, Wei, Zhang, Yimin, Pandey, Mahesh D.
• Format: Article
• Language: English
• Subjects: Computer simulation; Copula; Entropy; Fractional moments; Maximum entropy; Modelling; Probabilistic lifetime modelling; Probabilistic methods; Probability theory; Reliability engineering; Stochastic systems; Structural reliability; Studies; System reliability analysis; Useful life
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2017.07.036

•This paper presents a fractional moment method for probabilistic lifetime modelling of engineering systems.•Factional moments are calculated based on a small, simulated sample of remaining useful life of the system.•The principle of maximum entropy (MaxEnt) with fractional moments is used to recover the system lifetime distribution.•Applications of method are illustrated by several dynamical and discontinuous stochastic systems. 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.