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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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    1. Hao, Songhua & Yang, Jun & Berenguer, Christophe, 2019. "Degradation analysis based on an extended inverse Gaussian process model with skew-normal random effects and measurement errors," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 261-270.
    2. Massimiliano Giorgio & Fabio Postiglione & Gianpaolo Pulcini, 2020. "Bayesian estimation and prediction for the transformed Wiener degradation process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(4), pages 660-678, July.
    3. Zhi‐Sheng Ye & Min Xie, 2015. "Rejoinder to ‘Stochastic modelling and analysis of degradation for highly reliable products’," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 35-36, January.
    4. Zhi‐Sheng Ye & Min Xie, 2015. "Stochastic modelling and analysis of degradation for highly reliable products," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(1), pages 16-32, January.
    5. Massimiliano Giorgio & Agostino Mele & Gianpaolo Pulcini, 2019. "A perturbed gamma degradation process with degradation dependent non‐Gaussian measurement errors," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(2), pages 198-210, March.
    6. Wang, Xiaofei & Wang, Bing Xing & Jiang, Pei Hua & Hong, Yili, 2020. "Accurate reliability inference based on Wiener process with random effects for degradation data," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    7. Pulcini, Gianpaolo, 2016. "A perturbed gamma process with statistically dependent measurement errors," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 296-306.
    8. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    9. Chen, Zhen & Pan, Ershun & Xia, Tangbin & Li, Yanting, 2020. "Optimal degradation-based burn-in policy using Tweedie exponential-dispersion process model with measurement errors," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    10. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    11. Giorgio, Massimiliano & Pulcini, Gianpaolo, 2018. "A new state-dependent degradation process and related model misidentification problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1027-1038.
    12. Li, Junxing & Wang, Zhihua & Zhang, Yongbo & Liu, Chengrui & Fu, Huimin, 2018. "A nonlinear Wiener process degradation model with autoregressive errors," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 48-57.
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    2. Pang, Zhenan & Li, Tianmei & Pei, Hong & Si, Xiaosheng, 2023. "A condition-based prognostic approach for age- and state-dependent partially observable nonlinear degrading system," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
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    5. Chen, Wen-Bin & Li, Xiao-Yang & Kang, Rui, 2022. "Integration for degradation analysis with multi-source ADT datasets considering dataset discrepancies and epistemic uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 222(C).

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