IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v195y2020ics0951832019301085.html
   My bibliography  Save this article

Mis-specification analysis of Wiener degradation models by using f-divergence with outliers

Author

Listed:
  • Zhang, Fode
  • Ng, Hon Keung Tony
  • Shi, Yimin

Abstract

Degradation models have been investigated extensively for the evaluation of the quality and reliability of highly reliable products. In practical applications, the proper model of a degradation dataset is often unknown and misspecified for one thing; the dataset may be contaminated or contains outliers for another. Here, contamination means the degradation measurements are inspected embedded by noise with different levels. Thus, it is necessary to discuss the model mis-specification analysis and degradation data analysis when the degradation measurements contain outliers. Information geometry is a theory of using modern differential geometry to investigate the structure of manifolds induced by the statistical models, and the f-divergence is a popular tool in information geometry. This paper focuses on the model mis-specification analysis by employing the f-divergence as a tool to measure the difference between the true model and suggested models. A robust parameter estimation method based on minimizing the f-divergence is proposed. The results based on Kullback–Leibler divergence are obtained as an illustration. Simulation results and two numerical examples are used to illustrate the advantages of the proposed methodologies.

Suggested Citation

  • Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2020. "Mis-specification analysis of Wiener degradation models by using f-divergence with outliers," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:reensy:v:195:y:2020:i:c:s0951832019301085
    DOI: 10.1016/j.ress.2019.106751
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832019301085
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2019.106751?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Le Son, Khanh & Fouladirad, Mitra & Barros, Anne & Levrat, Eric & Iung, Benoît, 2013. "Remaining useful life estimation based on stochastic deterioration models: A comparative study," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 165-175.
    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. Wang, Xiaolin & Balakrishnan, Narayanaswamy & Guo, Bo, 2014. "Residual life estimation based on a generalized Wiener degradation process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 13-23.
    4. Peng, Weiwen & Li, Yan-Feng & Yang, Yuan-Jian & Huang, Hong-Zhong & Zuo, Ming J., 2014. "Inverse Gaussian process models for degradation analysis: A Bayesian perspective," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 175-189.
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    7. Wen, Yuxin & Wu, Jianguo & Das, Devashish & Tseng, Tzu-Liang(Bill), 2018. "Degradation modeling and RUL prediction using Wiener process subject to multiple change points and unit heterogeneity," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 113-124.
    8. Liu, Bin & Wu, Shaomin & Xie, Min & Kuo, Way, 2017. "A condition-based maintenance policy for degrading systems with age- and state-dependent operating cost," European Journal of Operational Research, Elsevier, vol. 263(3), pages 879-887.
    9. Xu, Ancha & Shen, Lijuan, 2018. "Improved on-line estimation for gamma process," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 67-73.
    10. Alberto Cena & Giovanni Pistone, 2007. "Exponential statistical manifold," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(1), pages 27-56, March.
    11. Fode Zhang & Hon Keung Tony Ng & Yimin Shi & Ruibing Wang, 2019. "Amari–Chentsov structure on the statistical manifold of models for accelerated life tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 77-105, March.
    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.
    13. Ling, M.H. & Ng, H.K.T. & Tsui, K.L., 2019. "Bayesian and likelihood inferences on remaining useful life in two-phase degradation models under gamma process," Reliability Engineering and System Safety, Elsevier, vol. 184(C), pages 77-85.
    14. Zhou, Jingke & Zhu, Lixing, 2016. "Principal minimax support vector machine for sufficient dimension reduction with contaminated data," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 33-48.
    15. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    16. Ye, Zhi-Sheng & Chen, Nan & Shen, Yan, 2015. "A new class of Wiener process models for degradation analysis," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 58-67.
    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. Hui Xiao & Kunxiang Yi & Gang Kou & Liudong Xing, 2020. "Reliability of a two‐dimensional demand‐based networked system with multistate components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(6), pages 453-468, September.
    2. Wang, Jiaolong & Zhang, Fode & Zhang, Jianchuan & Liu, Wen & Zhou, Kuang, 2023. "A flexible RUL prediction method based on poly-cell LSTM with applications to lithium battery data," Reliability Engineering and System Safety, Elsevier, vol. 231(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. Yan, Bingxin & Ma, Xiaobing & Yang, Li & Wang, Han & Wu, Tianyi, 2020. "A novel degradation-rate-volatility related effect Wiener process model with its extension to accelerated ageing data analysis," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. 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).
    3. 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.
    4. 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.
    5. 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).
    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. Zhang, Jian-Xun & Hu, Chang-Hua & He, Xiao & Si, Xiao-Sheng & Liu, Yang & Zhou, Dong-Hua, 2017. "Lifetime prognostics for deteriorating systems with time-varying random jumps," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 338-350.
    8. Xudan Chen & Guoxun Ji & Xinli Sun & Zhen Li, 2019. "Inverse Gaussian–based model with measurement errors for degradation analysis," Journal of Risk and Reliability, , vol. 233(6), pages 1086-1098, December.
    9. 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).
    10. Hu, Changhua & Xing, Yuanxing & Du, Dangbo & Si, Xiaosheng & Zhang, Jianxun, 2023. "Remaining useful life estimation for two-phase nonlinear degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    11. Le Liu & Xiao-Yang Li & Enrico Zio & Rui Kang & Tong-Min Jiang, 2017. "Model Uncertainty in Accelerated Degradation Testing Analysis," Post-Print hal-01652218, HAL.
    12. Cai, Xiao & Li, Naipeng & Xie, Min, 2024. "RUL prediction for two-phase degrading systems considering physical damage observations," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    13. Guo, Jingbo & Wang, Changxi & Cabrera, Javier & Elsayed, Elsayed A., 2018. "Improved inverse Gaussian process and bootstrap: Degradation and reliability metrics," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 269-277.
    14. 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).
    15. Wang, Huan & Wang, Guan-jun & Duan, Feng-jun, 2016. "Planning of step-stress accelerated degradation test based on the inverse Gaussian process," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 97-105.
    16. Wang, Zhijie & Zhai, Qingqing & Chen, Piao, 2021. "Degradation modeling considering unit-to-unit heterogeneity-A general model and comparative study," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    17. Liu, Di & Wang, Shaoping, 2020. "A degradation modeling and reliability estimation method based on Wiener process and evidential variable," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    18. Ye, Zhi-Sheng & Chen, Nan & Shen, Yan, 2015. "A new class of Wiener process models for degradation analysis," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 58-67.
    19. Hachem, Hassan & Vu, Hai Canh & Fouladirad, Mitra, 2024. "Different methods for RUL prediction considering sensor degradation," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    20. Lin, Chun Pang & Ling, Man Ho & Cabrera, Javier & Yang, Fangfang & Yu, Denis Yau Wai & Tsui, Kwok Leung, 2021. "Prognostics for lithium-ion batteries using a two-phase gamma degradation process model," Reliability Engineering and System Safety, Elsevier, vol. 214(C).

    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:eee:reensy:v:195:y:2020:i:c:s0951832019301085. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.