Degradation modeling with subpopulation heterogeneities based on the inverse Gaussian process |
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| Affiliation: | 1. Department of Statistics, Zhejiang Gongshang University, China;2. Department of Industrial and Systems Engineering, National University of Singapore, Singapore;3. School of Economics, Nanjing University of Finance and Economics, China;1. Yunnan Innovation Institute, Beihang University, Kunming 650233, China;2. School of Reliability and Systems Engineering, Beihang University, Beijing 100083, China;1. School of Statistics, East China Normal University, Shanghai 200241, PR China;2. Department of Industrial Engineering, Hanyang University, Seoul, 04763, Korea;3. School of Statistics, Shandong University of Finance and Economics, Jinan, 250014, PR China;1. School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin, China;2. College of Electrical and Electronic Engineering, Wenzhou University, Zhejiang, China;3. Energy Department, Politecnico di Milano, Italy;4. MINES ParisTech, PSL Research University, CRC, Sophia Antipolis, France;5. Aramis Srl, Via pergolesi 5, Milano, Italy;6. Department of Nuclear Engineering, College of Engineering, Kyung Hee University, South Korea |
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| Abstract: | This study proposes a random effects model based on inverse Gaussian process, where the mixture normal distribution is used to account for both unit-specific and subpopulation-specific heterogeneities. The proposed model can capture heterogeneities due to subpopulations in the same population or the units from different batches. A new Expectation-Maximization (EM) algorithm is developed for point estimation and the bias-corrected bootstrap is used for interval estimation. We show that the EM algorithm updates the parameters based on the gradient of the loglikelihood function via a projection matrix. In addition, the convergence rate depends on the condition number that can be obtained by the projection matrix and the Hessian matrix of the loglikelihood function. A simulation study is conducted to assess the proposed model and the inference methods, and two real degradation datasets are analyzed for illustration. |
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