A generalized dynamic stress-strength interference model under δ-failure criterion for self-healing protective structure

Traditional dynamic stress-strength interference (SSI) models usually assume that a failure occurs when the magnitude of a shock exceeds the strength. The assumption holds in most circumstances, while it is not applicable for self-healing protective structure which go through a recovery process after each shock. In this paper, a generalized dynamic SSI model combined with the δ-failure criterion is proposed to analyze the reliability for self-healing protective structure. Particularly, the shock is modeled as a non-homogenous Poisson process with stochastic time-varying magnitude, and the strength is modeled as a stochastic degradation path. Two different initial states (i.e., intact state and healing state) are considered under the δ-failure criterion. Then, a Gauss-Legendre-based hierarchical iteration algorithm is established to solve the complex reliability function including multiple internal and external nested integrations. Numerical solutions which can significantly improve the computational efficiency are provided. Finally, a simulation study and a real application to spur gear reducer are provided to illustrate the effectiveness of the proposed model and method.