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The two dependent competing risks are soft failure due to aging degradation and fragmentation caused by shocks and hard failure due to spring breakage caused by the same shock process. Considering the complexity of the product itself and the instability of the working environment, this study proposed a generalized reliability model for systems experiencing dependent competing failure processes (DCFPs) of degradation and random shocks, which considered two kinds of DCFP: (1) shock process could affect soft failure thresholds; (2) degradation process could affect hard failure thresholds. In case (1), we considered the effect that a cumulative number of shocks above a certain magnitude could have on the change in the soft failure threshold. In case (2), we considered not only the shock process's impact on the soft failure threshold but also the total degradation (including continuous degradation and sudden degradation caused by shock) on the hard failure threshold. The model captures the features that the shocks experienced by the system affect the degradation process, accelerating the system degradation and causing soft failures; the degradation process of the system affects the shock process, making the system more susceptible to failure from external shocks. Finally, an example using micro‐electro‐mechanical systems devices illustrates the effectiveness of the proposed approach with sensitivity analysis. [ABSTRACT FROM AUTHOR]

This paper investigated reliability modeling for systems subject to dependent competing risks considering that variation of the failure threshold is not considered in most studies on competing failure reliability. Firstly, the variation of degradation quantity under shocks was analyzed, and the variation of the threshold was considered on this basis. Secondly, the cumulative degradation under the influence of the random shock process was analyzed. The attractive property of Copula functions is symmetry. Then, a linear Wiener process model was applied to model performance degradation failure, and a multi-performance degradation correlated-competition model based on a Copula function was constructed, which considered the correlated competition between multi-performance degradation failures. Lastly, a micromotor system was used to analyze the applicability of the proposed model for bivariate instances, demonstrating the rationality and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

This article develops reliability models for systems subject to two dependent competing failure processes, considering the correlation between additional damage size on degradation in soft failure process and stress magnitude of shock load in hard failure process, both of which are caused by the same kth random shock. The generalized correlative reliability assessment model based on copulas is proposed, which is then extended to three different shock patterns: (1) δ‐shock, (2) m‐shock, and (3) m‐run shocks. There are some statistical works to be introduced in reliability modeling, including data separation of total degradation amount, inferring the distribution of amount of aging continuous degradation at time t, and fitting copula to the specific correlation. The developed reliability models are demonstrated for an application example of a micro‐electro‐mechanical system. [ABSTRACT FROM AUTHOR]