Browsing by Author "Shu, Yin"

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    Markov Additive Processes for Degradation with Jumps under Dynamic Environments
    (National Science Foundation, 2021) Shu, Yin; Feng, Qianmei; Kao, Edward P. C.; Coit, David W.; Liu, Hao; Biostatistics and Health Data Science, School of Medicine
    We use general Markov additive processes (Markov modulated Lévy processes) to integrally handle the complexity of degradation including internally- and externally-induced stochastic properties with complex jump mechanisms. The background component of the Markov additive process is a Markov chain defined on a finite state space; the additive component evolves as a Lévy subordinator under a certain background state, and may have instantaneous nonnegative jumps occurring at the time the background state switches. We derive the Fokker-Planck equations for such Markov modulated processes, based on which we derive Laplace expressions for reliability function and lifetime moments, represented by the infinitesimal generator matrices of Markov chain and the Lévy measure of Lévy subordinator. The superiority of our models is their flexibility in modeling degradation data with jumps under dynamic environments. Numerical experiments are used to demonstrate that our general models perform well.
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    Using Degradation-with-Jump Measures to Estimate Life Characteristics of Lithium-Ion Battery
    (Elsevier, 2019-11) Shu, Yin; Feng, Qianmei; Liu, Hao; Biostatistics, School of Public Health
    Degradation-with-jump measures are time series data sets containing the information of both continuous and randomly jumping degradation evolution of a system. Traditional maximum likelihood estimation and Bayesian estimation are not convenient for such general jump processes without closed-form distributions. Based on general degradation models derived using Lévy driven non-Gaussian Ornstein-Uhlenbeck (OU) processes, we propose a systematic statistical method using linear programing estimators and empirical characteristic functions. The point estimates of reliability function and lifetime moments are obtained by deriving their explicit expressions. We also construct bootstrap procedures for the confidence intervals. Simulation studies for a stable process and a stable driven OU process are performed. In the case study, we use a general Lévy process to fit the Li-ion battery life data, and then estimate the reliability and lifetime moments of the battery. By integrally analyzing degradation data series embedded with jump measures, our work provides the efficient and precise estimation for life characteristics.