Reliability modeling and analysis of competitive failure systems based on inverse Gaussian degradation

Engineering systems operating in random environments are frequently subjected to the coupled effects of internal degradation and external random shocks, giving rise to diverse failure modes. Consequently, reliability analysis of competing failure systems holds considerable significance. To address the limitations of existing research on shock-induced Inverse Gaussian (IG) degradation models, this study employs the IG process to characterize the natural degradation behavior of the system. Meanwhile, a generalized Pólya process (GPP)—which is capable of capturing non-stationary, non-independent increments and historical dependence—is adopted to model the shock arrival process. Under an extreme shock mechanism, a competing failure reliability model integrating the IG process and GPP is established. In the proposed model, when the shock magnitude exceeds a predefined threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> </mml:math> , shocks may directly trigger hard failure; concurrently, they induce additional degradation increments, which lead to soft failure once the cumulative degradation surpasses the threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> </mml:math> . Leveraging the independent increment property of the IG process and the law of iterated expectations, key reliability indices are derived analytically, including system reliability, mean time to failure, expected number of shocks prior to failure, as well as the probabilities of soft and hard failures. Finally, a lithium-ion battery case study combined with Monte Carlo simulations is conducted to validate the effectiveness of the developed model, and a systematic investigation is performed to quantify the impacts of model parameters on system reliability performance.