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1. Multi-dimensional Lévy Processes for Multiple Dependent Degradation Processes in Lifetime Analysis

   Shi, Y; Shu, Y; Feng, Q. (May 2018, Proceedings of Industrial and Systems Engineering Research Conference)

   The analysis of multiple dependent degradation processes is a challenging research work in the reliability field, especially for complex degradation with random jumps. To integrally handle the jump uncertainties in degradation and the dependence among degradation processes, we construct multi-dimensional Lévy processes to describe multiple dependent degradation processes in engineering systems. The evolution of each degradation process can be modeled by a one-dimensional Lévy subordinator with a marginal Lévy measure, and the dependence among all dimensions can be described by Lévy copulas and the associated multiple-dimensional Lévy measure. This Lévy measure is obtained from all its one-dimensional marginal Lévy measures and the Lévy copula. We develop the Fokker-Planck equations to describe the probability density in stochastic systems. The Laplace transforms of both reliability function and lifetime moments are derived. Numerical examples are used to demonstrate our models in lifetime analysis. 

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2. Quality assessment and lifetime prediction of base metal electrode multilayer ceramic capacitors: Challenges and opportunities

   https://doi.org/10.1016/j.pedc.2023.100045  

   Yousefian, Pedram; Randall, Clive A. (October 2023, Power Electronic Devices and Components)

   Base metal electrode (BME) multilayer ceramic capacitors (MLCCs) are widely used in aerospace, medical, military, and communication applications, emphasizing the need for high reliability. The ongoing advancements in BaTiO3-based MLCC technology have facilitated further miniaturization and improved capacitive volumetric density for both low and high voltage devices. However, concerns persist regarding infant mortality failures and long-term reliability under higher fields and temperatures. To address these concerns, a comprehensive understanding of the mechanisms underlying insulation resistance degradation is crucial. Furthermore, there is a need to develop effective screening procedures during MLCC production and improve the accuracy of mean time to failure (MTTF) predictions. This article reviews our findings on the effect of the burn-in test, a common quality control process, on the dynamics of oxygen vacancies within BME MLCCs. These findings reveal the burn-in test has a negative impact on the lifetime and reliability of BME MLCCS. Moreover, the limitations of existing lifetime prediction models for BME MLCCs are discussed, emphasizing the need for improved MTTF predictions by employing a physics-based machine learning model to overcome the existing models’ limitations. The article also discusses the new physical-based machine learning model that has been developed. While data limitations remain a challenge, the physics-based machine learning approach offers promising results for MTTF prediction in MLCCs, contributing to improved lifetime predictions. Furthermore, the article acknowledges the limitations of relying solely on MTTF to predict MLCCs’ lifetime and emphasizes the importance of developing comprehensive prediction models that predict the entire distribution of failures. 

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3. Global planning of accelerated degradation tests based on exponential dispersion degradation models

   https://doi.org/10.1002/nav.21923  

   Lee, I‐Chen; Tseng, Sheng‐Tsaing; Hong, Yili (July 2020, Naval Research Logistics (NRL))

   Abstract The accelerated degradation test (ADT) is an efficient tool for assessing the lifetime information of highly reliable products. However, conducting an ADT is very expensive. Therefore, how to conduct a cost‐constrained ADT plan is a great challenging issue for reliability analysts. By taking the experimental cost into consideration, this paper proposes a semi‐analytical procedure to determine the total sample size, testing stress levels, the measurement frequencies, and the number of measurements (within a degradation path) globally under a class of exponential dispersion degradation models. The proposed method is also extended to determine the global planning of a three‐level compromise plan. The advantage of the proposed method not only provides better design insights for conducting an ADT plan, but also provides an efficient algorithm to obtain a cost‐constrained ADT plan, compared with conventional optimal plans by grid search algorithms. 

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4. Predicting Average Product Lifetime Using Physics-Based Gaussian Process Method in Early Design Stage

   https://doi.org/10.1115/DETC2020-22199  

   Wei, Xinpeng; Han, Daoru; Du, Xiaoping (August 2020, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   null (Ed.)

   Abstract Average lifetime, or mean time to failure (MTTF), of a product is an important metric to measure the product reliability. Current methods of evaluating MTTF are mainly statistics or data based. They need lifetime testing on a number of products to get the lifetime samples, which are then used to estimate MTTF. The lifetime testing, however, is expensive in terms of both time and cost. The efficiency is also low because it cannot be effectively incorporated in the early design stage where many physics-based models are available. We propose to predict MTTF in the design stage by means of physics-based models. The advantage is that the design can be continually improved by changing design variables until reliability measures, including MTTF, are satisfied. Since the physics-based models are usually computationally demanding, we face a problem with both big data (on the model input side) and small data (on the model output side). We develop an adaptive supervised training method based on Gaussian process regression, and the method can then quickly predict MTTF with minimized number of calling the physics-based models. The effectiveness of the method is demonstrated by two examples. 

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5. Physics-Informed Data-Driven Approaches to Electric Vehicle Battery State-of-Health Prediction: Comparison of Parallel and Series Configurations

   https://doi.org/10.1115/1.4068697  

   Zhao, Yixin; Haapala, Karl R; Natarajan, Arun; Behdad, Sara (September 2025, Journal of Computing and Information Science in Engineering)

   Abstract Battery lifetime and reliability depend on accurate state-of-health (SOH) estimation, while complex degradation mechanisms and varying operating conditions strengthen this challenge. This study presents two physics-informed neural network (PINN) configurations, PINN-parallel and PINN-series, designed to improve SOH prediction by combining an equivalent circuit model (ECM) with a long short-term memory (LSTM) network. PINN-parallel process inputs data through parallel ECM and LSTM modules and combines their outputs for SOH estimation. On the other hand, the PINN-series uses a sequential approach that feeds ECM-derived parameters into the LSTM network to supplement temporal data analysis with physics information. Both models utilize easily accessible voltage, current, and temperature data that match realistic battery monitoring constraints. Experimental evaluations show that the PINN-series outperforms the PINN-parallel and the baseline LSTM model in accuracy and robustness. It also adapts well to different input conditions. This demonstrates that the simulated battery dynamic states from ECM increase the LSTM's ability to capture degradation patterns and improve the model's ability to explain complex battery behavior. However, a trade-off between the robustness and training efficiency of PINNs is identified. The research outcomes show the potential of PINN models (particularly the PINN-series) in advancing battery management systems, although they require considerable computational resources. 

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