Reliability analysis of gear rotation meta-action unit based on Weibull and inverse Gaussian competing failure process

•Describing the hard failure process by the Weibull distribution.•Describing the wear degradation process of gear by IG process.•Taking into account the interaction between hard failure and soft failure.•Proposing a mixed δ-extreme shock model.•Establishing a competing failure process of a GRMAU.•Providing a scheme for the failure process analyses of other MAUs. In order to analyze the reliability of meta-action unit(MAU) from the perspective of competing failure, this paper proposes a reliability analysis method for gear rotation MAU (GRMAU) subjected to the competing failure process of wear degradation and random shocks. For the traditional competing failure process, Winner process and Gamma process were widely used to describe soft failure, Poisson process was widely used to describe hard failure. In this paper, hard failure is described by the Weibull distribution, which can handle the case that the shocks count data are under-dispersion or over-dispersion, and soft failure is described by the inverse Gaussian(IG) process, which is suitable for the degradation process that is monotonically increasing and that degraded mean and variance have certain randomness. Moreover, a mixed δ-extreme shock model is proposed to extend the traditional shock models. Taking into account the interaction between the two failure forms, the reliability analyses of the mutually dependent competing failure process based on the four shock models, namely extreme shock model, cumulative shock model, δ shock model and mixed δ-extreme shock model, are carried out. Finally, some numerical examples vis-à-vis a GRMAU are illustrated to explain the implementation and effectiveness of the proposed model.