IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i21p2740-d666865.html
   My bibliography  Save this article

Objective Bayesian Estimation for Tweedie Exponential Dispersion Process

Author

Listed:
  • Weian Yan

    (School of Transportation and Logistics, East China Jiaotong University, Nanchang 330013, China
    School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China)

  • Shijie Zhang

    (School of Transportation and Logistics, East China Jiaotong University, Nanchang 330013, China)

  • Weidong Liu

    (School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063, China)

  • Yingxia Yu

    (School of Transportation and Logistics, East China Jiaotong University, Nanchang 330013, China)

Abstract

An objective Bayesian method for the Tweedie Exponential Dispersion (TED) process model is proposed in this paper. The TED process is a generalized stochastic process, including some famous stochastic processes (e.g., Wiener, Gamma, and Inverse Gaussian processes) as special cases. This characteristic model of several types of process, to be more generic, is of particular use for degradation data analysis. At present, the estimation methods of the TED model are the subjective Bayesian method or the frequentist method. However, some products may not have historical information for reference and the sample size is small, which will lead to a dilemma for the frequentist method and subjective Bayesian method. Therefore, we propose an objective Bayesian method to analyze the TED model. Furthermore, we prove that the corresponding posterior distributions have nice properties and propose Metropolis–Hastings algorithms for the Bayesian inference. To illustrate the applicability and advantages of the TED model and objective Bayesian method, we compare the objective Bayesian estimates with the subjective Bayesian estimates and the maximum likelihood estimates according to Monte Carlo simulations. Finally, a case of GaAs laser data is used to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Weian Yan & Shijie Zhang & Weidong Liu & Yingxia Yu, 2021. "Objective Bayesian Estimation for Tweedie Exponential Dispersion Process," Mathematics, MDPI, vol. 9(21), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2740-:d:666865
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/21/2740/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/21/2740/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cholette, Michael E. & Yu, Hongyang & Borghesani, Pietro & Ma, Lin & Kent, Geoff, 2019. "Degradation modeling and condition-based maintenance of boiler heat exchangers using gamma processes," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 184-196.
    2. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    3. Weian Yan & David Bigaud & Nadare Matoiri Chaibati & Laurent Izoret, 2020. "Optimization of Accelerated Destructive Degradation Testing of Cementitious Materials for Their Performances Qualification under Aggressive Environments: The Case of Carbonation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-19, April.
    4. 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.
    5. 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.
    6. Weian Yan & Hassen Riahi & Karim Benzarti & Robert Chlela & Laurence Curtil & David Bigaud, 2021. "Durability and Reliability Estimation of Flax Fiber Reinforced Composites Using Tweedie Exponential Dispersion Degradation Process," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-21, February.
    7. Daojiang He & Yunpeng Wang & Mingxiang Cao, 2018. "Objective Bayesian analysis for the accelerated degradation model using Wiener process with measurement errors," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 2(1), pages 27-36, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Weidong & Xu, Ben & Liu, Yan & Li, Shaoshuai & Yan, Weian, 2024. "A field-function methodology predicting the service lifetime of photovoltaic modules," Renewable and Sustainable Energy Reviews, Elsevier, vol. 192(C).
    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhou, Shirong & Tang, Yincai & Xu, Ancha, 2021. "A generalized Wiener process with dependent degradation rate and volatility and time-varying mean-to-variance ratio," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Truong-Ba, Huy & Cholette, Michael E. & Rebello, Sinda & Kent, Geoff, 2024. "Joint planning of inspection, replacement, and component decommissioning for a series system with non-identically degrading components," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    3. Zhang, Ao & Wang, Zhihua & Bao, Rui & Liu, Chengrui & Wu, Qiong & Cao, Shihao, 2023. "A novel failure time estimation method for degradation analysis based on general nonlinear Wiener processes," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    4. Sun, Fuqiang & Fu, Fangyou & Liao, Haitao & Xu, Dan, 2020. "Analysis of multivariate dependent accelerated degradation data using a random-effect general Wiener process and D-vine Copula," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    5. Wang, Xiaolin & Liu, Bin & Zhao, Xiujie, 2021. "A performance-based warranty for products subject to competing hard and soft failures," International Journal of Production Economics, Elsevier, vol. 233(C).
    6. Chang, Miaoxin & Huang, Xianzhen & Coolen, Frank PA & Coolen-Maturi, Tahani, 2023. "New reliability model for complex systems based on stochastic processes and survival signature," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1349-1364.
    7. Liang, Qingzhu & Yang, Yinghao & Peng, Changhong, 2023. "A reliability model for systems subject to mutually dependent degradation processes and random shocks under dynamic environments," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    8. Zhang, Jian-Xun & Si, Xiao-Sheng & Du, Dang-Bo & Hu, Chang-Hua & Hu, Chen, 2020. "A novel iterative approach of lifetime estimation for standby systems with deteriorating spare parts," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    9. 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).
    10. 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.
    11. Pang, Zhenan & Si, Xiaosheng & Hu, Changhua & Du, Dangbo & Pei, Hong, 2021. "A Bayesian Inference for Remaining Useful Life Estimation by Fusing Accelerated Degradation Data and Condition Monitoring Data," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    12. Song, Kai & Cui, Lirong, 2022. "A common random effect induced bivariate gamma degradation process with application to remaining useful life prediction," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    13. Pedersen, Tom Ivar & Vatn, Jørn, 2022. "Optimizing a condition-based maintenance policy by taking the preferences of a risk-averse decision maker into account," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    14. Fang, Guanqi & Pan, Rong & Hong, Yili, 2020. "Copula-based reliability analysis of degrading systems with dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    15. Luo, Yi & Zhao, Xiujie & Liu, Bin & He, Shuguang, 2024. "Condition-based maintenance policy for systems under dynamic environment," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    16. Dong, Qinglai & Cui, Lirong, 2019. "A study on stochastic degradation process models under different types of failure Thresholds," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 202-212.
    17. Zhang, Shuyi & Zhai, Qingqing & Li, Yaqiu, 2023. "Degradation modeling and RUL prediction with Wiener process considering measurable and unobservable external impacts," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    18. Giovanni Rinaldi & Philipp R. Thies & Lars Johanning, 2021. "Current Status and Future Trends in the Operation and Maintenance of Offshore Wind Turbines: A Review," Energies, MDPI, vol. 14(9), pages 1-28, April.
    19. Liao, Guobo & Yin, Hongpeng & Chen, Min & Lin, Zheng, 2021. "Remaining useful life prediction for multi-phase deteriorating process based on Wiener process," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    20. Zhao, Xiujie & Chen, Piao & Lv, Shanshan & He, Zhen, 2023. "Reliability testing for product return prediction," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1349-1363.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2740-:d:666865. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.