Random-Effect Models for Degradation Analysis Based on Nonlinear Tweedie Exponential-Dispersion Processes

The degradation data of highly reliable products are usually analyzed by stochastic process models, such as Wiener process, gamma process and inverse Gaussian process models. If such a specific degradation model is wrongly assumed, then poor analysis results of reliability assessment would be obtain...

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Published in:IEEE transactions on reliability Vol. 71; no. 1; pp. 47 - 62
Main Authors: Chen, Zhen, Xia, Tangbin, Li, Yaping, Pan, Ershun
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Analytical models
Biological system modeling
Degradation
Degradation analysis
Dispersion
Evolutionary algorithms
Evolutionary computation
exponential-dispersion (ED) process
Gaussian process
Inference algorithms
Mathematical model
Mathematical models
nonlinearity
Numerical models
parameter estimation
Parameters
random effects
Reliability analysis
Stochastic processes
ISSN:0018-9529, 1558-1721
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Abstract The degradation data of highly reliable products are usually analyzed by stochastic process models, such as Wiener process, gamma process and inverse Gaussian process models. If such a specific degradation model is wrongly assumed, then poor analysis results of reliability assessment would be obtained. Therefore, a class of exponential-dispersion processes, named Tweedie exponential-dispersion process (TEDP), is proposed to describe the products' degradation paths. The TEDP model which comprises the aforementioned stochastic processes as its special cases, is more flexible and applicable for degradation modeling. Considering the nonlinear characteristics of degradation paths and the unit-to-unit variability among the product units, random-effect models are established based on the nonlinear TEDP models with random drift and dispersion parameters. To improve the mathematical tractability of these models, the variational inference, expectation maximization algorithm and differential evolution algorithm are used to estimate the unknown model parameters. Furthermore, two nonlinear TEDP models with accelerated factors and random effects are developed for accelerated degradation analysis. Finally, a simulation study and three real applications are presented to show the effectiveness and superiority of the proposed models and methods.
AbstractList The degradation data of highly reliable products are usually analyzed by stochastic process models, such as Wiener process, gamma process and inverse Gaussian process models. If such a specific degradation model is wrongly assumed, then poor analysis results of reliability assessment would be obtained. Therefore, a class of exponential-dispersion processes, named Tweedie exponential-dispersion process (TEDP), is proposed to describe the products' degradation paths. The TEDP model which comprises the aforementioned stochastic processes as its special cases, is more flexible and applicable for degradation modeling. Considering the nonlinear characteristics of degradation paths and the unit-to-unit variability among the product units, random-effect models are established based on the nonlinear TEDP models with random drift and dispersion parameters. To improve the mathematical tractability of these models, the variational inference, expectation maximization algorithm and differential evolution algorithm are used to estimate the unknown model parameters. Furthermore, two nonlinear TEDP models with accelerated factors and random effects are developed for accelerated degradation analysis. Finally, a simulation study and three real applications are presented to show the effectiveness and superiority of the proposed models and methods.
Author Chen, Zhen
Pan, Ershun
Xia, Tangbin
Li, Yaping
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SubjectTerms Analytical models
Biological system modeling
Degradation
Degradation analysis
Dispersion
Evolutionary algorithms
Evolutionary computation
exponential-dispersion (ED) process
Gaussian process
Inference algorithms
Mathematical model
Mathematical models
nonlinearity
Numerical models
parameter estimation
Parameters
random effects
Reliability analysis
Stochastic processes
Title Random-Effect Models for Degradation Analysis Based on Nonlinear Tweedie Exponential-Dispersion Processes
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