Remaining Useful Life Analysis for Two‐Stage Nonlinear Inverse Gaussian Process With Random Effects

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ABSTRACTEvaluating the reliability of high‐reliability, long‐life products remains a central challenge in the realm of reliability engineering. The intricate internal structure of these products results in a performance degradation process that is both nonlinear and multi‐staged. Distinguished from the traditional single‐stage degradation model, the two‐stage degradation model requires consideration of the degradation state at a critical transition point. This complexity significantly complicates the task of modeling and predicting the remaining useful life (RUL) for products exhibiting two‐stage nonlinear degradation. To address this challenge, this paper introduces a novel two‐stage inverse Gaussian (IG) degradation process model. This model builds upon and extends the traditional nonlinear IG degradation process model, incorporating a two‐stage approach to account for the uncertainty at the degradation transition point and randomizing the drift coefficients to better reflect the stochastic nature of the degradation process. The analytical expressions of probability density functions (PDF) and reliability functions are derived based on the definition of first hitting time (FHT). The unknown parameters of the model are estimated using the Gibbs sampling method within the Markov Chain Monte Carlo (MCMC) framework. The applicability and effectiveness of our proposed method are substantiated through a simulation example and by analyzing real‐world degradation data from a cabin door lock mechanism.