## 1 Introduction
ADTs offer a more time-efficient approach by accelerating degradation through increased stress and employing models to predict the system's lifetime. Two primary approaches are used in degradation modeling: black-box and white-box [11]. The white-box approach analyzes individual components and their interactions, whereas the black-box approach treats the system as a single unit, focusing on output trends. [PERSON] et al. [12] used a model based on thermodynamic and electrode kinetic principles to analyze 7000 h of dura bility evaluation data collected under a constant current of 8 mA/cm\({}^{2}\). The Particle Filter (PF) algorithm was applied to predict the RUL (Remaining Useful Life), and it was found that during the lifespan of the FC, catalyst degradation contributed to 84.3% of the voltage degradation. However, owing to the inherent complexity of PEMFC stacks, the black-box approach is often favored, and various models have been employed. [PERSON] et al. [13] applied a bi-exponential model to predict the PEMFC stack degradation. Subsequently, [PERSON] et al. [14] enhanced it by integrating a hierarchical Bayesian framework to enhance the reliability of the PEMFC stack system. [PERSON] et al. [15] employed a deep-learning approach, called the grid long short-term memory recurrent neural network, to investigate the performance degradation and predict the lifetime of multiple stacks, including 1.2 kW Ballard Nexa and Proton Motor 200 (PM 200) 25-kW fuel cells. Accurate lifetime prediction requires substantial degradation data, which can be time-consuming to acquire under normal operating conditions. Therefore, accelerated testing, coupled with appropriate data interpretation for normal conditions, is essential. The Arrhenius model provides a framework for quantifying the influence of temperature on degradation rates [16, 17]. [PERSON] et al. [18] conducted ADTs on direct methanol fuel cells at 60, 70, and 80 \({}^{\circ}\)C to predict their lifespans and employed the Weibull-Arrhenius model to predict lifetime under normal conditions. Specifically, they applied a step-by-step approach to fit the model to the ADT data. This study introduces a novel single-step approach for analyzing ADT data obtained from PEMFC stacks operated at two different temperatures. An Arrhenius-based bi-exponential mixed-effects model was developed, integrating the bi-exponential degradation, Arrhenius, and a non-linear mixed-effects (NLME) model. This approach allows for the simultaneous determination of both fixed and random effects within the model parameters. The remainder of the paper is organized as follows: Section 2 presents the durability test protocol, bi-exponential model for characterizing cell-voltage degradation, application of the Arrhenius model as an acceleration factor, and determination of fixed- and random-effects parameters using the NLME model. Section 3 investigates the degradation of the PEMFC stack under different temperatures and analyzes the acceleration factor through the parameter estimation of the ADT data. Based on the estimated parameter values, we conducted Monte Carlo simulations to predict the failure-time distribution. Finally, Section 4 concludes the paper and presents directions for future research.