The Gamma constant-stress accelerated degradation model is a natural model for monotonous degradation processes. However, unit heterogeneity often exists in practice, necessitating a more realistic model. This study develops a Gamma process with random effects to accurately capture accelerated degradation data for reliability analysis, encompassing both point and interval estimation. First, the Expectation-Maximization (EM) algorithm is developed to obtain point estimates of the proposed model. Since these estimates are sensitive to initial values, potentially impacting the outcomes, an improved EM algorithm is proposed, which iteratively refines the estimation quality by executing two different M-steps, thereby enhancing overall estimation accuracy. Secondly, given the complexity of the model and the constraint of small sample sizes and limited stress levels, a three-step interval estimation method is devised. This method segregates the parameters into three distinct parts and addresses them individually using the generalized pivotal quantity method, which simplifies the parameter interval estimation process and enhances the estimation accuracy. Finally, simulation studies and a real example of O-rings are presented to demonstrate the effectiveness of the proposed method.

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The prediction of remaining useful life (RUL) is a critical component of prognostic and health management for industrial systems. In recent decades, there has been a surge of interest in RUL prediction based on degradation data of a well-defined degradation index (DI). However, in many real-world applications, the DI may not be readily available and must be constructed from complex source data, rendering many existing methods inapplicable. Motivated by multivariate sensor data from industrial induction motors, this paper proposes a novel prognostic framework that develops a nonlinear DI, serving as an ensemble of representative features, and employs a similarity-based method for RUL prediction. The proposed framework enables online prediction of RUL by dynamically updating information from the in-service unit. Simulation studies and a case study on three-phase industrial induction motors demonstrate that the proposed framework can effectively extract reliability information from various channels and predict RUL with high accuracy.@en