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Bayesian analysis for the transformed exponential dispersion process with random effects

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  • Duan, Fengjun
  • Wang, Guanjun

Abstract

The basic exponential-dispersion (ED) process can be used to describe many degradation phenomena, but its degradation increments are only age-dependent, which limits its application especially for the phenomena with state-dependent degradation increments. This paper proposes a transformed ED (TED) process degradation model with both age- and state-dependent increments, which is an extended model including the basic ED process model as a special case. The mean and variance functions of the TED process are derived, and the variance-to-mean ratio of the TED process is no longer a constant. Besides, the random effect is introduced into the TED degradation process model to describe the heterogeneity among different units. For the TED process with and without random effects, the Bayesian MCMC algorithm is applied to estimate the model parameters. Further, an approximation method based on moment generating function is used to evaluate the lifetime and remaining useful life (RUL) distribution of products based on the fixed effect and random effect TED process models. Finally, a numerical example of GaAs laser is used to illustrate the effectiveness of the proposed models and methods. The results show that the proposed TED process has better performance for this degradation data set compared with existing process models.

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  • Duan, Fengjun & Wang, Guanjun, 2022. "Bayesian analysis for the transformed exponential dispersion process with random effects," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    • Handle: RePEc:eee:reensy:v:217:y:2022:i:c:s0951832021005986
    DOI: 10.1016/j.ress.2021.108104
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    References listed on IDEAS

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    2. Yan, Weian & Xu, Xiaofan & Bigaud, David & Cao, Wenqin, 2023. "Optimal design of step-stress accelerated degradation tests based on the Tweedie exponential dispersion process," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
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    5. Fan, Linchuan & Chai, Yi & Chen, Xiaolong, 2022. "Trend attention fully convolutional network for remaining useful life estimation," Reliability Engineering and System Safety, Elsevier, vol. 225(C).

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