Degradation Modeling Using Stochastic Processes With Random Initial Degradation

In degradation tests, it is common to see that the initial degradation levels of test units are heterogeneous. Moreover, the degradation rate of a path may also be correlated with the initial value of the degradation measure. Motivated by this observation, in this paper, we introduce a time shift to...

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Vydáno v:	IEEE transactions on reliability Ročník 68; číslo 4; s. 1320 - 1329
Hlavní autoři:	Shen, Lijuan, Wang, Yudong, Zhai, Qingqing, Tang, Yincai
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.12.2019 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Analytical models Computer simulation Correlation Data models Degradation Error analysis Estimation Expectation–maximization (EM) algorithm Gallium arsenide lasers Gaussian distribution Gaussian process maximum likelihood estimation Modelling random initial degradation random-effects model Stochastic models stochastic process models Stochastic processes
ISSN:	0018-9529, 1558-1721
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Abstract	In degradation tests, it is common to see that the initial degradation levels of test units are heterogeneous. Moreover, the degradation rate of a path may also be correlated with the initial value of the degradation measure. Motivated by this observation, in this paper, we introduce a time shift to the traditional stochastic process models, which presumes that the product has experienced some degradation at the beginning of the test. Such a modeling technique can also capture the correlation between the initial degradation and the degradation rate, when the degradation rate of each path does vary from unit to unit. We apply this technique to the three popular stochastic process models, i.e., the Wiener process, the gamma process, and the inverse Gaussian process, and develop the corresponding parameter inference procedures. Monte Carlo simulations are implemented to validate the proposed models and the estimation procedures. Applications to the degradation analysis of block error rates data and GaAs laser data reveal good performance of the proposed models.
AbstractList	In degradation tests, it is common to see that the initial degradation levels of test units are heterogeneous. Moreover, the degradation rate of a path may also be correlated with the initial value of the degradation measure. Motivated by this observation, in this paper, we introduce a time shift to the traditional stochastic process models, which presumes that the product has experienced some degradation at the beginning of the test. Such a modeling technique can also capture the correlation between the initial degradation and the degradation rate, when the degradation rate of each path does vary from unit to unit. We apply this technique to the three popular stochastic process models, i.e., the Wiener process, the gamma process, and the inverse Gaussian process, and develop the corresponding parameter inference procedures. Monte Carlo simulations are implemented to validate the proposed models and the estimation procedures. Applications to the degradation analysis of block error rates data and GaAs laser data reveal good performance of the proposed models.
Author	Shen, Lijuan Tang, Yincai Zhai, Qingqing Wang, Yudong
Author_xml	– sequence: 1 givenname: Lijuan orcidid: 0000-0002-3906-4250 surname: Shen fullname: Shen, Lijuan email: isesl@nus.edu.sg organization: Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore – sequence: 2 givenname: Yudong surname: Wang fullname: Wang, Yudong email: yudongw@u.nus.edu organization: Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore – sequence: 3 givenname: Qingqing orcidid: 0000-0001-6549-6906 surname: Zhai fullname: Zhai, Qingqing email: zhaiqing59@126.com organization: School of Management, Shanghai University, Shanghai, China – sequence: 4 givenname: Yincai orcidid: 0000-0001-6756-6461 surname: Tang fullname: Tang, Yincai email: yctang@stat.ecnu.edu.cn organization: School of Statistics, East China Normal University, Shanghai, China
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SubjectTerms	Analytical models Computer simulation Correlation Data models Degradation Error analysis Estimation Expectation–maximization (EM) algorithm Gallium arsenide lasers Gaussian distribution Gaussian process maximum likelihood estimation Modelling random initial degradation random-effects model Stochastic models stochastic process models Stochastic processes
Title	Degradation Modeling Using Stochastic Processes With Random Initial Degradation
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