Reliability analysis for continuous degrading systems subject to multi-level failure dependence

This article explicitly models multi-level failure dependence existing in continuous degrading systems with multiple degrading components. Dependence within the component level is specified as that arrived shocks increase the vulnerability to inherent degradation. Dependence among components refers to the fact that the degradation of a particular component can be accelerated by others. The Gamma process is employed as a comprehensive framework for modeling the dependence above. A compound Poisson process and normal distribution are both introduced to describe the stochastic characteristics of random shocks. Procedures for obtaining analytical solutions and simulation results of reliability analysis are both presented. At last, an illustrative example of a hydraulic system is studied to demonstrate the effectiveness and advantages of the proposed method.