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.

Battery lifetime prediction is crucial in industrial applications. However, the lack of diversity in training data often poses challenges regarding the robustness and generalization of lifetime predictions for batteries from different batches. Motivated by the early cycle data from lithium-ion batteries, this article proposes a robust transfer learning method by employing a model average framework, where the weights are determined based on the distance between the source domain and the target domain. Kernel regression is used to build the prediction of battery lifetime using early cycle data, and transfer component analysis is utilized to transfer knowledge between different domains. The case study on lithium-ion phosphate/graphite cells demonstrates that the proposed method can mitigate the impact of negative transfer and has superior performance compared to traditional methods.